Area of a Circle

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GED Math › Area of a Circle

Questions 1 - 10

1

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

2

Let $\pi = 3.14$

Find the area of a circle with a diameter of 8in.

$50.24\text{in}^2$

$200.96\text{in}^2$

$25.12\text{in}^2$

$153.86\text{in}^2$

$100.48\text{in}^2$

Explanation

To find the area of a circle, we will use the following formula:

$A = \pi \cdot r^2$

where r is the radius of the circle.

Now, we know $\pi = 3.14$ . We know the diameter of the circle is 8in. We know the diameter is two times the radius. Therefore, the radius is 4in. So, we substitute. We get

$A = 3.14 \cdot(4\text{in})^2$

$A = 3.14 \cdot 16\text{in}^2$

$A = 50.24\text{in}^2$

3

Find the area of a circle with a radius of 25.

$625 \pi$

$125\pi$

$150\pi$

$525\pi$

$50\pi$

Explanation

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (25)^2 = \pi (25)(25) = 625 \pi$

The answer is: $625 \pi$

4

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: $\pi$

5

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: $100\pi$

6

If the circumference of a circle is , what is the area of the circle in square inches? Use $\pi=3.14$ .

Explanation

Recall how to find the circumference of a circle.

$\text{Circumference}=2\pi r$ , where is the radius.

Plug in the given circumference and solve for the radius.

$50.24=2\pi r$

Next, recall how to find the area of a circle.

$\text{Area}=\pi r^2$

Plug in the given radius to find the area.

$\text{Area}=(3.14)(8)^2=200.96$

7

Determine the area of a circle with a radius of $9\sqrt{2}$ .

$162\pi$

$81\pi$

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

Explanation

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (9\sqrt{2})^2=\pi (9\sqrt{2})(9\sqrt{2}) = 81\cdot 2 \pi$

The answer is: $162\pi$

8

Determine the area of a circle with a radius of .

$64\pi x^2$

$64\pi ^2x^2$

$16\pi ^2x^2$

$16\pi x^2$

Explanation

Write the formula for the area of a circle.

$A =\pi r^2$

Substitute the known radius.

$A =\pi (8x)^2=\pi (8x)(8x)$

The answer is: $64\pi x^2$

9

Give the area of a circle with circumference $22 \pi$ .

$121 \pi$

$81 \pi$

$162 \pi$

$242 \pi$

Explanation

The radius of a circle can be determined by dividing its circumference by $2 \pi$ :

$r = \frac{C}{2 \pi }$

Set $C = 22\pi$ and evaluate :

$r = \frac{22 \pi}{2 \pi } = 11$

Now substitute 11 for in the area formula for a circle:

$A = \pi r^{2}$

$A = \pi \cdot 11^{2 }$

$A = 121 \pi$ square untis.

10

Find the area of the circle with a circumference of $20\pi$ .

$100\pi$

$50\pi$

$400\pi$

$20\pi$

$200\pi$

Explanation

Write the formula for the circumference of a circle.

$C = 2\pi r$

Substitute the circumference into the equation.

$20\pi= 2\pi r$

Divide both sides by $2\pi$ .

$\frac{20\pi}{2\pi}= \frac{2\pi r}{2\pi}$

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

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

The answer is: $100\pi$

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