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