shape and space
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SHAPE AND SPACE
Circles
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LET US DEFINE CIRCLE
A ___________is a simple shape that is the set of all points in a plane that are at a given distance from a given point, the center.
A circle is a simple shape that is the set of all points in a plane that are at a given distance from a given point, the center.
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Radius is the distance from the center to the edge of a circle. Radius is half of the diameter
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Diameter is a segment that passes through the center and has its endpoints on the circle. The diameter is twice the length of the radius
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THE VALUE OF
We use the symbol π because the number cannot be written exactly.
π = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 (to 200 decimal places)!
𝝅
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In circles the AREA is equal to 3.14 ( ) times the radius (r) to the power of 2.
Thus the formula looks like: A= r2
In circles the circumference is formula looks like:
2 r
𝝅
𝝅
𝝅
The circumference of a circle is the actual length around the circle which is equal to 360°.
π is equal to 3.14.
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THE CIRCUMFERENCE OF A CIRCLE
Use π = 3.14 to find the circumference of this circle.
C = 2πr8 cm
= 2 × 4
= 8π
R = 4
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THE CIRCUMFERENCE OF A CIRCLE
Use π = 3.14 to find the circumference of the following circles:
C = 2πr4 cm
= 2 × 2
= 4π cm
C = 2πr9 m
= 2 × π × 9
= 18π m
C = 2πr
= 2 × 12
= 12π mm
C = 2πr58 cm
= 2 × π × 58
= 116π cm
24mm
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FORMULA FOR THE AREA OF A CIRCLE
We can find the area of a circle using the formula
radius
Area of a circle = πr2
Area of a circle = π × r × r
or
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AREA OF A CIRCLE
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THE CIRCUMFERENCE OF A CIRCLE
Use π = 3.14 to find the area of this circle.
A = πr24 cm
= π × 4 × 4
= 16π cm2
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THE AREA OF A CIRCLE
Use π = 3.14 to find the area of the following circles:
A = πr22 cm
= π × 22
= 4π cm2
A = πr2
10 m= π × 52
= 25π m2
A = πr2
23 mm = π × 232
= 529π mm2
A = πr2
78 cm= π × 392
= 1521π cm2
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FIND THE AREA OF THIS SHAPE
Use π = 3.14 to find area of this shape.
The area of this shape is made up of the area of a circle of diameter 12cm and the area of a rectangle of width 6cm and length 12cm.
6 cm12 cm Area of circle = π × 62
= 36π cm2
Area of rectangle = 6 × 12
= 78 cm2
Total area = 36π + 78
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?
FINDING THE RADIUS GIVEN THE CIRCUMFERENCE
Use π = 3.14 to find the radius of this circle.
C = 2πr12 cm
How can we rearrange this to make r the subject of the formula?
r =C
2π
12
2 × π=
6π=
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FIND THE PERIMETER OF THIS SHAPE
Use π = 3.14 to find perimeter of this shape.
The perimeter of this shape is made up of the circumference of a circle of diameter 13 cm and two lines of length 6 cm.
6 cm14 cm
Perimeter = 14 x 6
Circumference = 2πr
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CIRCUMFERENCE PROBLEM
The diameter of a bicycle wheel is 50 cm. How many complete rotations does it make over a distance of 1 km?
50 cm
The circumference of the wheel
= π × 50
Using C = 2πr and π = 3.14,
= 157 cm
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