perimeter, area and volume
DESCRIPTION
Perimeter, Area and Volume. Grades F to A. Rectangles and Triangles. Hyperlinks!. Counting Squares. Parallelograms and Trapeziums. Area – working backwards. Circles. Compound Shapes. Volume of cuboids. Volume of prisms. Surface area. Sectors of circles. - PowerPoint PPT PresentationTRANSCRIPT
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Perimeter, Area and Volume
Grades F to A
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Hyperlinks!
Counting Squares
Area – working
backwardsCircles
Volume of cuboids
Sectors of circlesSurface area
Volume of prisms
Volume and surface area of complex
shapes
Rectangles and Triangles
Parallelograms and
Trapeziums
Compound Shapes
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 4: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/4.jpg)
Area and perimeter by counting and measuring
How do I find the area and perimeter of a shape?
Grade F
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 6: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/6.jpg)
What are perimeter and area?
Perimeter is the length around the outside of a shape.
Area is the space inside a shape.
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Example
The rectangle has a perimeter of:
The rectangle has a area of:
5 + 3 5 + 3+ = 16cm
5 × 3 = 15cm²
5 + 5 = 15cm²5 +Take note of
the units!
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Find the perimeter and area of this rectangle:
Perimeter =
Area =
20cm
24cm²
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 10: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/10.jpg)
Rectangles and Triangles
Can I calculate the perimeter and area of a rectangle and triangle?
Grade E
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
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The formulae to remember:•
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Two examples:Example 1
Find the area and perimeter of this rectangle:
Area = 8 × 6Area = 48cm²
Perimeter = 8 + 6 + 8 + 6Perimeter = 28cm
Example 2Find the area of this triangle:
Area = 5 × 12 ÷ 2Area = 60cm² ÷ 2
Area = 30cm²
6cm
8cm
5cm13cm
12cm
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Have a go at some:Question 1
Find the area of this triangle:Question 2
Find the perimeter and area of this rectangle:
10cm
11cm
8cm7cm
Answer: 35cm²Answer:
Area = 88cm²Perimeter = 38cm
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
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Parallelograms and Trapeziums
Can I calculate the area of a parallelogram and trapezium?
Grade D
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
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The formulae:•
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Two examplesExample 1
Find the area of this parallelogram:
Area = 7 × 5Area = 35cm²
Example 2
•
7cm
5cm 6cm 5cm
4cm
8cm
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Have a go at a couple of questions:Question 1
Find the area of this parallelogram:
Question 2
Find the area of this trapezium:
12cm
8cm10cm 7cm
9cm
11cm
Answer: 96cm²Answer: 70cm²
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
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Circles
Can I find the circumference and area of a circle?
Grade C
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 24: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/24.jpg)
Names to do with circles you must remember:
Radius
Diameter
Chord
Tangent
Circumference
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Formulae you need to remember:
•
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A couple of examplesExample 1
Find the circumference and area of a circle with a diameter
of 10cm to 1 dp.
Circumference = π × 10Circumference = 31.4cm
Area = π × 5²Area = 78.5cm²
Example 2Find the circumference and
area of a circle with a radius of 8cm to 1 dp.
Circumference = π × 16Circumference = 50.3cm
Area = π × 8²Area = 201.1cm²
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Some for you to try:Question 1
Find the circumference and area of this circle to 1 dp.
Question 2Find the circumference and
area of a circular pond with a diameter of 3m to 1 dp.
Circumference = 88.0cmArea = 615.8cm²
Circumference = 9.4mArea = 7.1m²
14cm
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
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Area – Working Backwards
Now you can find the area of shapes, can you find a length having been
given the area?
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Formulae Reminder:•
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Find the missing lengths:
Area = 48cm²Area = 21cm²
Area = 32cm² Area = 28cm² Area = 113.1cm²
8cm
?cm 7cm
?cm
8cm
9cm
?cm
Diameter = ?Height = ? Height = 4cm
None of these are drawn to
scale
6cm
6cm
4cm
5cm
12cm
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 33: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/33.jpg)
Compound Shapes
Can I calculate the perimeter and area of a compound shape?
Grade C
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 35: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/35.jpg)
What is a compound shape?
A compound shape is a shape that is made up of lots of different shapes.
The key is to split the complex shape up into simpler shapes, find the areas of the simple
shapes then add your areas together.
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An exampleFind the area of this shape:
Split it up!
Area = 40 + 32 = 72cm²
12cm
8cm8cm
3cm
Area = 8×5 = 40cm²Area = 8×4
= 32cm²
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Another exampleFind the area of this shape:
Split it up!
Area = 54 + 13.5 = 67.5cm²
3m
9m
6m Area = 9×6 = 54m²
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A couple of questions:Question 1
Find the area of this shape:
Question 2
Find the area of this shape:
10m
8m
6cm
12cm
3cm
5cm
Answer: 66cm² Answer: 119.3m²
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 40: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/40.jpg)
Volume of Cuboids
Can I calculate the volume of a cuboid?Grade C
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 42: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/42.jpg)
How to calculate the volume of a cuboid:
•
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An example:Find the volume of this cuboid:
Volume = 3 × 5 × 4Volume = 60cm³
3cm
5cm4cm
Take note of the units!
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Another example, working backwards:
Find the height of this cuboid:
280cm³ = 10 × 7 × hh = 280 ÷ (10 × 7)
h = 4cm
10cm7cm
Volume = 280cm³
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Two questions to have a go at:
Question 1Find the volume of this cuboid:
Question 2The tank below contains exactly 100 litres of water. How far up the tank does the water go?
(Hint: 1 litre = 1000cm³)
5cm
8cm
6cm
1m0.5m
0.5m
Answer: 240cm³ Answer: 0.2m or 20cm
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 47: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/47.jpg)
Prisms
Can I calculate the volume of a prism?
Grade C
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 49: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/49.jpg)
What is a prism?
A prism is a 3D shape that has the same cross-section all the way through.
For example:
Triangular Prism Hexagonal Prism Cylinder
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Calculating the volume of a prism:
Find the area of the cross-section then multiply by the length.
Volume = Area of cross-section × length
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Two examplesExample 1
•
Example 2
If the volume of this prism is 360cm³ and it is 9cm long,
what is the area of the cross-section?
Area of cross-section = 360 ÷ 9Area of cross-section = 40cm²
8cm
3cm
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A couple of questions:Question 1
Find the volume of this triangular prism:
Question 2A circular pond contains
18,850 litres of water. It has a diameter of 4m. How deep is
the pond if it is a cylinder?(1 litre = 1000cm³)
8cm 12cm
9cm
Answer: 432cm³ Answer: 1.5m or 150cm
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 54: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/54.jpg)
Surface Area
Can I calculate the surface area of a cuboid or a triangular prism?
Grade C to B
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 56: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/56.jpg)
What is surface area?
The area of all the faces of a 3D shape added together.
You could think of it like this: it is the exact amount of wrapping paper you would need to
wrap your shape up with.
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Find the surface area of this cuboid:
Each face you can see has a face exactly the same opposite it.
2 × 4 × 10 = 80cm²2 × 4 × 5 = 40cm²
2 × 5 × 10 = 100cm²Total surface area = 220cm²
4cm
10cm5cm
4cm × 5cm = 20cm²5cm × 10cm = 50cm²
4cm × 10cm = 40cm²
There are two of each size of
rectangle
![Page 58: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/58.jpg)
Find the surface area of these two cuboids:
Cuboid 1
Answer: 258cm²
Cuboid 2
Answer: 192cm²
9cm
5cm6cm
4cm
12cm3cm
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A Triangular Prism Example:•
![Page 60: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/60.jpg)
A Cylinder Example:Find the surface area of this cylinder:
It’s two circles and a rectangle (whose length is the circumference of the circle):
Surface area = 2 × π × 4² + 5 × π × 8
Surface area = 226.2cm²
4cm5cm
The two circles The rectangle
![Page 61: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/61.jpg)
Find the surface area:
Answer: 527.8cm²
12cm
8cm
![Page 62: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/62.jpg)
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 63: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/63.jpg)
Sectors of Circles
Can I find the area of a sector and its arc length?
Grade B
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Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 65: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/65.jpg)
What is a sector?
A sector is a fraction of a circle – like a slice of cake or pizza.
It’s point is the centre of the circle.
The arc length is the curved part of the sector.
![Page 66: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/66.jpg)
The formulae:•
Area of a whole circle
Circumference of a whole circle
Angle given for the sector
![Page 67: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/67.jpg)
An exampleFind the area and arc length of this sector.
7cm
7cm50
Area:
Area = 21.4cm²
Arc Length:
Arc Length = 44.1cm
![Page 68: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/68.jpg)
A question for you:Find the area and perimeter of this sector.
(Don’t forget the “straight bits” for the perimeter!)
Area = 15.4cm² Perimeter = 15.7cm
4cm4cm 110
![Page 69: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/69.jpg)
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 70: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/70.jpg)
Volume and Surface Area of Complex Shapes
Can I use the formulae to find surface area and volume of cones and
spheres?Grade A
![Page 71: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/71.jpg)
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
![Page 72: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/72.jpg)
Some formulae for you:
• •
These formulae are at the front of the paper!
![Page 73: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/73.jpg)
And one more…
•
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Cone Example:• •
5cm
12cm 13cm
Circular base
Curved surface area
![Page 75: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/75.jpg)
Sphere Example:
• •
r = 6cm
![Page 76: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/76.jpg)
Two questionsQuestion 1
Find the volume and curved surface area of this cone:
Question 2
Find the volume and curved surface area of this sphere:
6cm
8cm 8cm
C.S.A. = 188.5cm² Volume = 301.6cm³
Surface area = 804.2cm² Volume = 2144.6cm³
![Page 77: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/77.jpg)
The frustumA frustum is a cone or pyramid that has had it’s
top chopped off!
Remember: the original cone/pyramid and the cone/pyramid that has been chopped off are similar, mean that the dimensions are in the
same ratio.
![Page 78: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/78.jpg)
Find the volume of the frustum:•
3cm
6cm
5cmDouble the radius, so
double the height
![Page 79: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/79.jpg)
Try this one:
Find the volume of this frustum:
3cm
9cm
8cm
Answer: 980.2cm³
![Page 80: Perimeter, Area and Volume](https://reader036.vdocuments.us/reader036/viewer/2022062310/56816770550346895ddc5a86/html5/thumbnails/80.jpg)
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.