GED Math - Circumference

Determine the circumference of a circle with a radius of $\frac{\pi}{4}$ .

$\frac{\pi ^2}{2}$

$\frac{\pi }{2}$

$\frac{\pi}{8}$

$\frac{\pi^2}{8}$

$\frac{1}{2}$

Explanation

Write the formula for the circumference of a circle.

$C=\2\pi r$

Substitute the radius.

$C=\2\pi (\frac{\pi}{4}) = \frac{\pi ^2}{2}$

The answer is: $\frac{\pi ^2}{2}$

What is the circumference of a circle with a diameter of 10 inches?

Explanation

The equation for the circumference of a circle is $C=2r\pi$ , where is the radius of the circle. The radius is half the diameter, or 5 inches.

$C=2(5)\pi$

$C=10\pi$

$\pi=3.14$

What is the circumference of a circle with an area of $12\pi$ ?

$4\pi\sqrt{3}$

$2\pi\sqrt{3}$

$\pi\sqrt{3}$

$2\sqrt{3}$

$6\pi\sqrt{3}$

Explanation

For this question, you need to first use the area to calculate your circle's radius. From that, you can then calculate the circumference of the circle. Recall that the area of a circle is defined as:

$A=\pi r^2$

For your data, this means:

$12\pi=\pi r^2$

Solving for , you get...

$r=\sqrt{12}=\sqrt{4*3}=2\sqrt{3}$

Now, the circumference of a circle is calculated as:

$C=2\pi r$

For your data, this is:

$C=2\pi*2\sqrt{3}=4\pi\sqrt{3}$

Find the circumference of a circle with an area of $36\pi.$

$12\pi$

$6 \pi$

$36 \pi$

$2 \pi$

$18 \pi$

Explanation

The problem is asking for us to solve for the circumference. However, the only provided information is the circle's area. In this kind of a problem, it's important think about how the provided information may relate to the information we need in order to solve for the problem.

The area of a circle is determined through the formula: $A=\pi r^2$ , where r is for radius.

The circumference of a circle is determined by the formula: $C= \pi d$ where d is diameter. It can also be written as $C=2\pi r$ because the radius is half the length of the diameter.

We can now easily see that the two concepts, area and circumference, are related through the variable r. Therefore, if we can solve for r from the area, we can use that to then solve for circumference.

$36\pi = \pi r^2$

$\frac{36 \pi}{\pi} = r^2$

Now that we have solved for the radius, we can use this value to "plug and chug" into the circumference formula and solve.

$C= 2 \pi (6)$

$C= 12 \pi$

Therefore, the circumference of the circle is $12\pi$ .

Identify the circumference of the circle with an area of $12 \pi$ .

$4\pi \sqrt{3}$

$2\pi \sqrt{3}$

$\frac{4\pi \sqrt{3}}{3}$

$\frac{2\pi \sqrt{3}}{3}$

$\frac{3\pi \sqrt{3}}{2}$

Explanation

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the area.

$12\pi=\pi r^2$

Square root both sides to find the radius.

$\sqrt{r^2}=\sqrt{12}$

$r=\sqrt{12} = \sqrt{4}\times \sqrt{3} = 2\sqrt{3}$

Write the formula for the circumference of the circle.

$C=2\pi r = 2\pi(2\sqrt{3}) = 4\pi \sqrt{3}$

The answer is: $4\pi \sqrt{3}$

What is the circumference of a circle with an area of $49\pi$ ?

$14\pi$

$12 \pi$

$7 \pi$

$13\pi$

$24.5 \pi$

Explanation

The area of a circle is determined through the formula: $A=\pi r^2$ , where r is for radius.

The circumference of a circle is determined by the formula: $C= \pi d$ where d is diameter. It can also be written as $C=2\pi r$ because the radius is half the length of the diameter.

$49\pi = \pi r^2$

$\frac{49 \pi}{\pi} = r^2$

Now that we have solved for the radius, we can use this value to "plug and chug" into the circumference formula and solve.

$C= 2 \pi (7)$

$C= 14 \pi$

Therefore, the circumference of the circle is $14\pi$ .

Circle 1

Give the circumference of the above circle.

$7 \pi$

$\frac{49 }{4}\pi$

$14 \pi$

$49 \pi$

Explanation

The circumference of a circle - the distance around it - can be found by multiplying its diameter by $\pi$ . The diameter of the circle is equal to 7, so the circumference is $7 \pi$ .