HOW TO FIND THE RADIUS FROM CIRCUMFERENCE

Examples 1-2 : Find the missing length in the circle.

Example 1 :

Solution :

The missing length in the above circle is radius.

Given : Circumference = 16π in.

2πr = 16π

Divide both sides by 2π.

r = 8

Radius = 8 in.

Example 2 :

Solution :

The missing length in the above circle is diameter.

Given : Circumference = 75.36 in.

2πr = 75.36

Substitute π = 3.14.

2(3.14)r = 75.36

6.28r = 75.36

Divide both sides by 6.28.

r = 12 in.

Diameter = 2 x Radius

= 2 x 12

= 24 in.

Example 3 :

A circular pond has a circumference of 628 feet. A model boat is moving directly across the pond, along a radius, at a rate of 5 feet per second. How long does it take the boat to get from the edge of the pond to the center ?

Solution :

Step 1 :

Find the radius of the pond.

Circumference = 628

2πr = 628

Substitute π = 3.14.

2(3.14)r = 628

6.28r = 628

Divide both sides by 6.28.

r = 100

Radius = 100 feet

Step 2 :

Find the time taken by the boat to get from the edge of the pond to the center along the radius.

Time = Distance/ Speed

= 100/5

= 20

Hence, the boat takes 20 seconds to get from the edge of the pond to the center.

Example 4 :

The circumference of a car wheel is 62.8 inches. Find its diameter.

Solution :

Diameter = 2 x Radius 

Step 1 :

Find the radius of the wheel.

Use the circumference formula. 

Circumference = 62.8

2πr = 62.8

Substitute π = 3.14.

2(3.14)r = 62.8

6.28r = 62.8

Divide both sides by 6.28.

r = 10

Radius = 10 in.

Step 2 :

Diameter = 2 x Radius

= 2 x 10 in.

= 20 in

Hence, diameter of the car wheel is 20 inches.

Example 5 :

The Ferris wheel can travel 2376 feet in one ride. If there are 12 revolutions in one ride, find the diameter of the wheel.

Solution :

Diameter = 2 x Radius

Step 1 :

Find the radius of the wheel.

1 ride = 2260.8 feet

12 revolutions = 2260.8 feet.

Divide both sides by 12.

1 revolution = 188.4 feet

Distance traveled in 1 revolution is equal to circumference of the Ferris wheel.

Circumference = 188.4

2πr = 188.4

Substitute π = 3.14.

2(3.14)r = 188.4

6.28r = 188.4

Divide both sides by 6.28.

r = 60

Radius = 60 feet

Step 2 :

Diameter = 2 x Radius

= 2 x 60 feet

= 60 feet

Hence, diameter of the Ferris wheel is 60 feet.

Example 6 :

A circular table top has a diameter of 85 cm. Work out the circumference of the table top.

Solution :

Diameter of the circle = 85 cm

Radius = 85/2

= 42.5

Circumference of the table top = 2πr

= 2 x 3.14 x 42.5

= 266.9 cm²

Example 7 :

The circle and the square have the same perimeter. Calculate the value of x.

Solution :

Perimeter of square = Circumference of circle

4a = 2πr

Here a is the side length and r is the radius.

4(60) = 2 ⋅ 3.14 ⋅ x

x = 240/(2⋅3.14)

x = 38.21

So, the radius of the circle is 38.21 cm

Example 8 :

A wheel has a diameter of 15 cm. The wheel travels 50 metres. How many complete revolutions does the wheel complete?

Solution :

Diameter = 15 cm

radius = 15/2

= 7.5 cm

Converting into meter,

1 m = 100 cm

1 cm = 1/100 m

7.5 cm = 7.5/100

= 0.075 m

Distance covered by the wheel = 50 m

Let n be the number of times the wheel is rotating.

n ⋅ 2πr = 50

n ⋅ 2 ⋅ 3.14 ⋅ 0.075 = 50

n ⋅ (0.471) = 50

n = 50/0.471

n = 106.15

Approximately 106 times.

Example 9 :

Calculate the perimeter of the pink shape.

Solution :

Perimeter of pink shape = Circumference of inner circular part + Circumference of outer circular part

Inner radius = 5/2

r = 2.5 cm

Outer radius = 8/2

R = 4 cm

= 2πR + 2πr

= 2π(R + r)

= 2 x 3.14 (4 + 2.5)

= 40.82 cm

Example 10 :

Nicole is a wedding organiser. The guests are to sit at circular tables with a diameter of 180 cm. Each guest needs 70 cm around the circumference of the table. There are 18 tables at the venue. A total of 145 guests are attending the wedding. Are there enough tables ?

Solution :

Calculating the circumference of the circular table

= 2πr

2r = 180 = diameter

= 3.14 x 180

= 565.2 cm

Each needs 70 cm around the circumference of the table.

= 565.2 / 70

= 8.07

Approximately 8 guests can sit in the table. Total number of tables is 18. Then,

= 18 x 8

= 144 guests

Since there are 145 guests, the space will not be enough.

Example 11 :

The area of a circle is 40 square cm. Calculate the circumference of the circle.

Solution :

Area of circle = 40 square cm

πr² = 40

3.14 x r² = 40

r² = 40/3.14

r² = 12.73

r = √12.73

r = 3.56

Circumference of circle = 2πr

= 2 x 3.14 x 3.56

= 22.35 cm

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