task 1 will allow you to practise the core formulae for ......li - to be able to calculate the...
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LI - To be able to calculate the volume and surface area of 3D objects using formulae.
This week in maths we will examine 3D shapes and learn to work out volume and surface
area.
Volume measures how much space a 3D object contains and surface area uses what we
have learned about 2D area, but on all of the surfaces that make up the 3D object.
The video below helps to explain this in a really straightforward way.
Note down the formulae as you watch and pay attention to the examples. Note: You do not
need to learn the information for spheres and cones (unless you find it very interesting).
https://www.youtube.com/watch?v=qJwecTgce6c
Once you have watched the video and feel confident about the information, you will have
four tasks that you m=can complete to practise these skills. Only task 1 is essential, so if you
are finding it difficult to make time, just do task 1.
Task 1 will allow you to practise the core formulae for volume and surface area
Task 2 will show that irregular prisms can still be worked with if the area of the irregular
side is known and allow you to practise with circular shapes
Task 3 will encourage you to use the formula for volume to work out missing information
Task 4 will allow you to practise finding volume and surface area for compound 3D shapes
Answers follow each task.
Email [email protected] with any questions about your work.
Task 1
This task is about using the formulae you learned from the video above and practising the steps
carefully. Answers are provided at the end.
Find the volume & surface area
Q1.
Q2.
Find the volume & surface area
Q1.
Q2.
4cm
4cm
8cm
3cm
3cm
5cm
Find the volume & surface area
Q1.
Q2.
Find the volume & surface area
Q1.
Q2.
5cm
5cm
5cm
4cm 10cm
6cm
6cm
6cm
5cm 8cm
Find the volume & surface area
Q1.
Q2.
Find the volume & surface area
Q1.
Q2.
6cm
4cm 5cm
8cm
7cm
3cm 4cm
10cm
Find the volume & surface area
Q1.
Q2.
Find the volume & surface area
Q1.
Q2.
5cm 4cm
2cm
6cm
10cm
6cm 5cm
3cm
5cm
7cm
Answers:
Cubes: (1) V – 125cm3 SA - 150cm2 (2) V – 64cm3 SA - 96cm2
Square ended cuboids: (1) V – 45cm3 SA - 78cm2 (2) V – 128cm3 SA - 160cm2
Cuboids: (1) V – 480cm3 SA - 376cm2 (2) V – 144cm3 SA - 192cm2
Equilateral triangular prism: (1) V – 100cm3 SA - 170cm2 (2) V – 120cm3 SA -
174cm2
Isosceles triangular prism: (1) V – 288m3 SA - 288m2 (2) V – 360m3 SA - 336m2
Parallelogram prism: (1) V – 192cm3 SA - 224cm2 (2) V – 210cm3 SA - 262cm2
Triangular prism: (1) V – 36m3 SA - 84m2 (2) V – 96m3 SA - 144cm2
Trapezium prism: (1) V – 160cm3 SA - 212cm2 (2) V – 140cm3 SA - 180cm2
Task 2
Section A
Calculate the volume of these prisms (note that the area of the
cross section is already done)
Section B
Calculate the volume of these prisms
Section C
Calculate the volume of these prisms
Extension (Challenge);
Answers – Volume of prism
Section A
1. 250 cm3
2. 510 cm3
3. 252 cm3
4. 4725 cm3
5. 132 m3
6. 480 m3
7. 186.76 m3
8. 60.68 m3
Section B
1. 90000 cm3
2. 252000 cm3
3. 18 m3
4. 36 m3
5. 96 cm3
6. 540 mm3
Section C
1. 140 cm3
2. 720 m3
3. 168 m3
4. 684 m3
Extension (Challenge)
i) Pi = 3.14 ii) pi(used on calculator)
1. i) 9043.2 cm3 ii) 9047.787cm3
2. i) 1538.6 cm3 ii) 1539.340 cm3
3. i) 276.9 cm3 ii) 277.088 cm3
4. i) 2034.7 cm3 ii) 2035.752 cm3
5. i) 763.0 cm3 ii) 763.40 cm3
6. a) 611.6 cm3 b) 212.1 cm3
c) 1194.6 cm3
Task 3
Find the length of each of these shapes.
19 cm2
Volume = 418 cm3
Volume = 224 cm3
Volume = 324 cm3
Volume = 168 cm3
Volume = 400 cm3
Volume = 270 cm3
Volume = 330 cm3
Volume = 255 cm3
a)
b)
c)
d)
e) f)
g) h)
16 cm2
9 cm2
12 cm2
5 cm2
30 cm2
22 cm2
17 cm2
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length
length
length
length
length
length
length
length
Answers
a. 22cm
b. 14cm
c. 36cm
d. 14cm
e. 80cm
f. 9cm
g. 15cm
h. 15cm
Task 4
Find the surface area and volume of these compound 3D shapes.
6cm
4cm
3cm
3cm
12cm
8cm 10cm
2.5cm 2.5cm
2.5cm 2.5cm
2cm
2cm
4cm
6cm
10cm
2m
2m
2m
1m
1m
4m
8m
7m 1m
1m
1.
2.
3.
Answers:
1. Surface area – 456cm2 Volume – 480cm3
2. Surface area – 408cm2 Volume – 280cm3
3. Surface area – 268cm2 Volume – 252cm3