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.

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