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ACT Math : Circles

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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 #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√5

π√2.5

5π

2.5π

None of the other answers

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:

$6\pi$

$3\pi$

$16\pi$

$9\pi$

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:

$196\pi$

$14\pi$

$21\pi$

$49\pi$

$3.5\pi$

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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Example Question #41 : Radius

What is the circumference of a circle with a radius of six ft? Leave your answer in terms of $\pi$ .

Possible Answers:

$24\pi$

$3\pi$

$9\pi$

$36\pi$

$12\pi ft$

Correct answer:

$12\pi ft$

Explanation:

To find the circumference given the radius, simply double the radius and mulitply by $\pi$ .

$C=2\pi r$

Thus:

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

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Example Question #42 : Radius

A running track can be formed by adding a semicircle to each of the short ends of a rectangle of dimension $100m\times20m$ .

If Tracy runs one lap around the track described above, how far has she run?

Possible Answers:

$100+10\pi\text{meters}$

$200+400\pi\text{meters}$

$240\text{meters}$

$200+20\pi\text{meters}$

$200+100\pi\text{meters}$

Correct answer:

$200+20\pi\text{meters}$

Explanation:

The questions really asks us to find the perimeter of the track.This would be the two long sides of the rectangle plus the circumferences of each of the two semicircles.

Each long side of the triangle is 100m .

Each semicircle has a circumference that is $\frac{1}{2}\pi d$ because the whole circumference is

$C=2\pi r$ thus the semicircle circumference would be half of that or,

$\frac{1}{2}2\pi r=\pi r$ and $r=\frac{1}{2}d$ .

Since the diameter of the semicircle is equal to the width of the rectangle, 20m . That means each semicircle has a circumference of $10\pi$ . Since we have two semicircles on the track, we can sum the two semicircle circumferences and the two long sides of the rectangle that comprise the track to get $200+20\pi$ .

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Example Question #581 : Act Math

Find the circumference of a circle with radius 6.

Possible Answers:

$6\pi$

$36\pi$

$12\pi$

$18\pi$

Correct answer:

$12\pi$

Explanation:

To solve, simply use the formula for the circumference of a circle.

In this particular case the radius of 6 should be substituted into the following equation to solve for the circumference.

Thus,

$C=2\pi{r}=2*\pi*6=12\pi$

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ACT Math : Circles

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find Circumference

Example Question #1 : 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

Example Question #41 : Radius

Example Question #42 : Radius

Example Question #581 : Act Math

All ACT Math Resources

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