Circles

Help Questions

GED Math › Circles

Questions 1 - 10

Find the area of a circle with a diameter of $5\pi$ .

$\frac{25}{4}\pi^3$

$\frac{25}{4}\pi^2$

$\frac{25}{2}\pi^3$

$\frac{25}{2}\pi^2$

$\textup{The answer is not given.}$

Explanation

Write the area of a circle.

$A=\pi r^2$

The radius is half the diameter.

$r= \frac{d}{2} = \frac{5\pi}{2}$

Substitute the radius into the equation.

$A=\pi (\frac{5\pi}{2})^2=\pi (\frac{5\pi}{2})(\frac{5\pi}{2})$

The answer is: $\frac{25}{4}\pi^3$

Determine the area of a circle with an diameter of .

$100\pi$

$400\pi$

$200\pi$

$1600\pi$

$800\pi$

Explanation

Write the formula for the area of a circle.

$A=\pi r^2$

The radius is half the diameter.

$A=\pi (10)^2 = 100\pi$

The answer is: $100\pi$

Determine the area of a circle in square feet with a radius of 12 inches.

$\pi$

$24\pi$

$2\pi$

$12\pi$

$144\pi$

Explanation

Write the formula for the area of a circle.

$A=\pi r^2$

Convert the radius to feet. There are 12 inches in a foot.

This means the radius in feet is 1.

Substitute the radius in feet to obtain the area in feet squared.

$A=\pi (1\textup{ ft})^2 = \pi \textup{ ft}^2$

The answer is: $\pi$

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 $12\pi$ .

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

$12\pi$

$6 \pi$

$36 \pi$

$2 \pi$

$18 \pi$

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.

$36\pi = \pi r^2$

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

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 $12\pi$ .

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:

$A=\pi r^2$