ACT Math - How to find circumference

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

$12\pi$

$6\pi$

$324\pi$

$6\pi^2$

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.

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

Find the circumference of a circle with radius 6.

$12\pi$

$36\pi$

$6\pi$

$18\pi$

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,

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

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

2√13_π_

√13_π_

26_π_

√26_π_

13_π_

Explanation

The formula for the area of a circle is A = _πr_2.

We are given the area, and by substitution we know that 13_π_ = _πr_2.

We divide out the π and are left with 13 = _r_2.

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

We find the circumference of the circle with the formula C = 2_πr_.

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

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?

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

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

$240\text{meters}$

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

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

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 .

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, . 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 $200+20\pi$ .

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

$9\pi$

$81\pi$

$18\pi$

$27\pi$

$90\pi$

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.

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

(x – 2)2 + (y + 3)2 = 9

$6\pi$

$9\pi$

$16\pi$

$3\pi$

Explanation

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

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

Leave your answer in terms of $\pi$ .

$14\pi$

$49\pi$

$196\pi$

$3.5\pi$

$21\pi$

Explanation

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

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

$12\pi ft$

$3\pi$

$36\pi$

$24\pi$

$9\pi$

Explanation

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

$C=2\pi r$

Thus:

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

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

6_π_

8_π_

10_π_

25_π_

12_π_

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 = 10_π_.

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

600π

3600π

300π

500π

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.

How to find circumference

Help Questions

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation