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GED Math : Area of a Circle

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Example Question #11 : Area Of A Circle

Determine the area of a circle if the radius is .

Possible Answers:

$1600\pi$

$80\pi$

$40\pi$

$400\pi$

$160\pi$

Correct answer:

$400\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

$A=\pi(20)^2 = 400\pi$

The answer is: $400\pi$

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Example Question #12 : Area Of A Circle

Find the area of a circle with a circumference of $100 \pi$ .

Possible Answers:

$250\pi$

$100\pi$

$1000\pi$

$2500\pi$

$500\pi$

Correct answer:

$2500\pi$

Explanation:

Write the formula for the circumference of a circle.

$C=2\pi r$

Substitute the circumference.

$100\pi=2\pi r$

Divide by $2\pi$ on both sides.

$\frac{100\pi}{2\pi}=\frac{2\pi r}{2\pi}$

r=50

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

$A=\pi (50)^2 = 2500\pi$

The answer is: $2500\pi$

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Example Question #13 : Area Of A Circle

What is the area of the circle with a diameter of ?

Possible Answers:

$36\pi$

$144\pi$

$18\pi$

$16\pi$

$72\pi$

Correct answer:

$36\pi$

Explanation:

Write the formula for the area of a circle.

$A= \pi r^2$

The radius is half the diameter.

$r= \frac{d}{2} = \frac{12}{2} = 6$

Substitute the radius into the equation.

$A= \pi( 6)^2 = 36\pi$

The answer is: $36\pi$

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Example Question #14 : Area Of A Circle

Find the area of a circle if the circumference is $16\pi^4$ .

Possible Answers:

$64\pi ^{10}$

$256\pi ^8$

$64\pi ^6$

$64\pi ^4$

$64\pi ^7$

Correct answer:

$64\pi ^7$

Explanation:

Write the formula for the circumference of a circle.

$C=2\pi r$

Substitute the circumference.

$16\pi^4 = 2\pi r$

Divide by $2\pi$ on both sides.

$\frac{16\pi^4 }{2\pi}= \frac{2\pi r}{2\pi}$

$r=8\pi ^3$

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (8\pi ^3)^2 = \pi(8\pi ^3)(8\pi ^3) =64\pi ^7$

The answer is: $64\pi ^7$

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Example Question #11 : Area Of A Circle

Determine the area of a circle with a radius of 15.

Possible Answers:

$125\pi$

$60\pi$

$225\pi$

$250\pi$

$30\pi$

Correct answer:

$225\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

$A=\pi (15)^2 = 225\pi$

The answer is: $225\pi$

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Example Question #16 : Area Of A Circle

Determine the area of a circle if the radius is $10\pi^2$ .

Possible Answers:

$100\pi ^4$

$100\pi ^5$

$20\pi ^3$

$10\pi^5$

$10\pi ^4$

Correct answer:

$100\pi ^5$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius into the equation.

$A=\pi (10\pi^2)^2 = 100\pi ^5$

The answer is: $100\pi ^5$

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Example Question #17 : Area Of A Circle

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

Possible Answers:

$24\pi$

$2\pi$

$12\pi$

$144\pi$

$\pi$

Correct answer:

$\pi$

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: $\pi$

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Example Question #18 : Area Of A Circle

Find the area of a circle with a diameter of 26cm.

Possible Answers:

$39\pi \text{ cm}^2$

$121\pi \text{ cm}^2$

$169\pi \text{ cm}^2$

$144\pi \text{ cm}^2$

$26\pi \text{ cm}^2$

Correct answer:

$169\pi \text{ cm}^2$

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 the diameter of the circle is 26cm. We also know the diameter is two times the radius. Therefore, the radius is 13cm.

So, we can substitute. We get

$A = \pi \cdot (13\text{cm})^2$

$A = \pi \cdot 169\text{cm}^2$

$A = 169\pi \text{ cm}^2$

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Example Question #19 : Area Of A Circle

Find the area of a circle with a radius of 12in.

Possible Answers:

$96\pi \text{ in}^2$

$100\pi \text{ in}^2$

$120\pi \text{ in}^2$

$121\pi \text{ in}^2$

$144\pi \text{ in}^2$

Correct answer:

$144\pi \text{ in}^2$

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 the radius of the circle is 12in. So, we can substitute. We get

$A = \pi \cdot (12\text{in})^2$

$A = \pi \cdot 144\text{in}^2$

$A = 144\pi \text{ in}^2$

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Example Question #11 : Area Of A Circle

If the diameter of circle is $2\frac{1}{2}$ , what must be the area?

Possible Answers:

$\frac{81}{16}\pi$

$25\pi$

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

$\frac{25}{16}\pi$

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

Correct answer:

$\frac{25}{16}\pi$

Explanation:

Convert the mixed fraction to an improper fraction by multiplying the denominator with the whole number and adding the numerator. The denominator stays constant.

$2\frac{1}{2}\rightarrow \frac{5}{2}$

Write the formula for the area of a circle.

$A=\pi r^2$

The radius is half the diameter.

$\frac{1}{2}\cdot \frac{5}{2} = \frac{5}{4}$

$A=\pi (\frac{5}{4})^2=\pi (\frac{5}{4}) (\frac{5}{4}) = \frac{25}{16}\pi$

The answer is: $\frac{25}{16}\pi$

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GED Math : Area of a Circle

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #11 : Area Of A Circle

Example Question #12 : Area Of A Circle

Example Question #13 : Area Of A Circle

Example Question #14 : Area Of A Circle

Example Question #11 : Area Of A Circle

Example Question #16 : Area Of A Circle

Example Question #17 : Area Of A Circle

Example Question #18 : Area Of A Circle

Example Question #19 : Area Of A Circle

Example Question #11 : Area Of A Circle

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