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ACT Math : How to find circumference

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Example Question #1 : Circumference Of A Circle

If a circle has an area of $81\pi$ , what is the circumference of the circle?

Possible Answers:

$9\pi$

$18\pi$

$90\pi$

$81\pi$

$27\pi$

Correct answer:

$18\pi$

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.

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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:

√26π

26π

√13π

13π

2√13π

Correct answer:

2√13π

Explanation:

The formula for the area of a circle is A = 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 C = 2πr.

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

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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:

12π

25π

8π

10π

6π

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.

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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?

Screen_shot_2013-03-18_at_4.54.03_pm

Possible Answers:

8π + 24

4π + 24

40 ft.

96 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.

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Example Question #2 : 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:

5π

π√2.5

None of the other answers

2.5π

π√5

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.

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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.

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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:

$6\pi$

$16\pi$

$9\pi$

$3\pi$

Correct answer:

$6\pi$

Explanation:

The radius is 3. Yielding a circumference of $6\pi$ .

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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 $\pi$ .

Possible Answers:

$196\pi$

$49\pi$

$3.5\pi$

$21\pi$

$14\pi$

Correct answer:

$14\pi$

Explanation:

Plug the radius into the circumference formula:
$\\ C = 2*\pi*r \newline C = 2 *\pi * 7 \newline C = 14\pi$

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Example Question #2 : How To Find Circumference

A circle has an area of $36\pi$ . Using this information find the circumference of the circle.

Possible Answers:

$324\pi$

$6\pi^2$

$6\pi$

$12\pi$

Correct answer:

$12\pi$

Explanation:

To find the circumference of a circle we use the formula

$C=2\pi*r$ .

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

$A=\pi*r^2$ .

So we manipulate that formula to solve for the radius.

$r=\sqrt{\frac{A}{\pi}}$ .

Then we plug in our given area.

$r=\sqrt{\frac{36\pi}{\pi}}=\sqrt{36}=6$ .

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

$C=2\pi*6=12\pi$ .

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Example Question #2 : How To Find Circumference

A circle has an area of $16\pi$ . Using this information find the circumference of the circle.

Possible Answers:

$16\pi$

$8\pi$

$4\pi$

$64\pi$

Correct answer:

$8\pi$

Explanation:

To find the circumference of a circle we use the formula

$C=2\pi*r$ .

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

$A=\pi*r^2$ .

So we manipulate that formula to solve for the radius.

$r=\sqrt{\frac{A}{\pi}}$ .

Then we plug in our given area.

$r=\sqrt{\frac{16\pi}{\pi}}=\sqrt{16}=4$ .

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

$C=2\pi*4=8\pi$ .

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ACT Math : How to find circumference

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Circumference Of A Circle

Example Question #1 : How To Find Circumference

Example Question #1 : How To Find Circumference

Example Question #1 : How To Find Circumference

Example Question #2 : How To Find Circumference

Example Question #4 : How To Find Circumference

Example Question #1 : How To Find Circumference

Example Question #1 : How To Find Circumference

Example Question #2 : How To Find Circumference

Example Question #2 : How To Find Circumference

All ACT Math Resources

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