**Using circumference to find radius :**

Given the circumference of a circle, we can use the appropriate circumference formula to find the radius or the diameter of the circle. We can use that information to solve problems.

**Example 1 : **

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.

Use the circumference formula.

C = 2πr

Substitute 628 for C and for 3.14 for π.

628 ≈ 2 x 3.14 x r

682 ≈ 6.28 x r

Divide both sides by 6.28

682/6.28 ≈ (6.28 x r)/6.28

100 ≈ r

The radius is about 100 feet.

**Step 2 :**

Find the time it takes the boat to get from the edge of the pond to the center along the radius.

Divide the radius of the pond by the speed of the model boat.

100 / 5 = 20

Hence, it takes the boat about 20 seconds to get to the center of the pond.

**Example 2 :**

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

**Solution : **

Diameter = 2 x Radius

**Step 1 : **

Find the radius of the wheel.

Use the circumference formula.

C = 2πr

Substitute 62.8 for C and for 3.14 for π.

62.8 ≈ 2 x 3.14 x r

62.8 ≈ 6.28 x r

Divide both sides by 6.28

62.8/6.28 ≈ (6.28 x r)/6.28

10 ≈ r

The radius is about 10 inches.

**Step 2 :**

Multiply the radius by 2 to find diameter of the wheel.

10 x 2 = 20

Hence, diameter of the car wheel is about 20 inches.

**Example 3 :**

The Ferris wheel can travel 2376 feet in one ride. If there are 12 revolutions in one ride, find the diameter of the wheel. Use π = 22/7.

**Solution : **

Diameter = 2 x Radius

**Step 1 :**

Find the radius of the wheel.

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

Then the distance traveled in 12 revolutions (one ride) is equal to 12 times circumference of the Ferris wheel.

So, we have

2376 = 12C

Divide both sides by 12.

2376/12 = 12C/12

198 = C

Use the circumference formula.

C = 2πr

Substitute 198 for C and for 22/7 for π.

198 ≈ 2 x (22/7) x r

198 ≈ (44/7) x r

Multiply both sides by 7/44

(7/44) x 198 ≈ (7/44) x (44/7) x r

31.5 ≈ r

The radius is about 31.5 feet.

**Step 2 :**

Multiply the radius by 2 to find diameter of the wheel.

31.5 x 2 = 63

Hence, diameter of the Ferris wheel is about 63 feet.

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