# ACT Math : How to find circumference

## Example Questions

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### Example Question #1 : Circumference Of A Circle

If a circle has an area of , what is the circumference of the circle?

Possible Answers:

Correct answer:

Explanation:

The formula for  the area of a circle is πr2. For this particular circle, the area is 81π, so 81π = πr2. Divide both sides by π and we are left with r2=81. Take the square root of both sides to find r=9. The formula for the circumference of the circle is 2πr = 2π(9) = 18π. The correct answer is 18π.

### Example Question #1 : How To Find Circumference

A circle with an area of 13π in2 is centered at point C. What is the circumference of this circle?

Possible Answers:

13π

√26π

√13π

2√13π

26π

Correct answer:

2√13π

Explanation:

The formula for the area of a circle is πr2.

We are given the area, and by substitution we know that 13π πr2.

We divide out the π and are left with 13 = r2.

We take the square root of r to find that r = √13.

We find the circumference of the circle with the formula = 2πr.

We then plug in our values to find = 2√13π.

### Example Question #1 : How To Find Circumference

A 6 by 8 rectangle is inscribed in a circle. What is the circumference of the circle?

Possible Answers:

25π

8π

6π

12π

10π

Correct answer:

10π

Explanation:

First you must draw the diagram. The diagonal of the rectangle is also the diameter of the circle. The diagonal is the hypotenuse of a multiple of 2 of a 3,4,5 triangle, and therefore is 10.
Circumference = π * diameter = 10π.

### Example Question #1 : How To Find Circumference

A gardener wants to build a fence around their garden shown below. How many feet of fencing will they need, if the length of the rectangular side is 12 and the width is 8?

Possible Answers:

96 ft

8π + 24

4π + 24

40 ft.

Correct answer:

8π + 24

Explanation:

The shape of the garden consists of a rectangle and two semi-circles. Since they are building a fence we need to find the perimeter. The perimeter of the length of the rectangle is 24. The perimeter or circumference of the circle can be found using the equation C=2π(r), where r= the radius of the circle. Since we have two semi-circles we can find the circumference of one whole circle with a radius of 4, which would be 8π.

### Example Question #1 : How To Find Circumference

The diameter of a circle is defined by the two points (2,5) and (4,6). What is the circumference of this circle?

Possible Answers:

π√2.5

None of the other answers

π√5

2.5π

Correct answer:

π√5

Explanation:

We first must calculate the distance between these two points. Recall that the distance formula is:√((x2 - x1)2 + (y2 - y1)2)

For us, it is therefore: √((4 - 2)2 + (6 - 5)2) = √((2)2 + (1)2) = √(4 + 1) = √5

If d = √5, the circumference of our circle is πd, or π√5.

### Example Question #4 : How To Find Circumference

A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?

Possible Answers:

3600π

500π

300π

600π

Correct answer:

600π

Explanation:

If the radius is 18 inches, the diameter is 3 feet. The circumference of the tire is therefore 3π by C=d(π). After 200 revolutions, the tire and car have gone 3π x 200 = 600π feet.

### Example Question #1 : How To Find Circumference

A circle has the equation below. What is the circumference of the circle?

(x – 2)2 + (y + 3)2 = 9

Possible Answers:

Correct answer:

Explanation:

The radius is 3. Yielding a circumference of .

### Example Question #1 : How To Find Circumference

What is the circumference of a cirle with a radius of seven?

Leave your answer in terms of .

Possible Answers:

Correct answer:

Explanation:

Plug the radius into the circumference formula:

### Example Question #2 : How To Find Circumference

A circle has an area of . Using this information find the circumference of the circle.

Possible Answers:

Correct answer:

Explanation:

To find the circumference of a circle we use the formula

.

In order to solve we must use the given area to find the radius. Area of a circle has a formula of

.

So we manipulate that formula to solve for the radius.

.

Then we plug in our given area.

.

Now we plug our radius into the circumference equation to get the final answer.

.

### Example Question #2 : How To Find Circumference

A circle has an area of . Using this information find the circumference of the circle.

Possible Answers:

Correct answer:

Explanation:

To find the circumference of a circle we use the formula

.

In order to solve we must use the given area to find the radius. Area of a circle has a formula of

.

So we manipulate that formula to solve for the radius.

.

Then we plug in our given area.

.

Now we plug our radius into the circumference equation to get the final answer.

.

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