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GED Math : Area of a Circle

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Example Question #31 : Area Of A Circle

Find the area of the circle with a radius of $\pi ^3$ .

Possible Answers:

$\pi^6$

$\pi ^7$

$\pi ^{10}$

$\pi ^4$

$\pi ^9$

Correct answer:

$\pi ^7$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

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

The answer is: $\pi ^7$

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Example Question #32 : Area Of A Circle

Find the area of a circle with a diameter of 2x^2 .

Possible Answers:

$\pi x^3$

4x^2

2x^4

$\pi x^4$

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

Correct answer:

$\pi x^4$

Explanation:

The radius of the circle is half the diameter, or x^2 .

Write the formula for the area of the circle.

$A= \pi r^2$

Substitute the radius.

$A= \pi (x^2)^2 = \pi (x^2)(x^2) = \pi x^4$

The answer is: $\pi x^4$

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Example Question #33 : Area Of A Circle

Determine the area of a circle with a diameter of $\pi^2$ .

Possible Answers:

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

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

$\pi^4$

$\frac{\pi^5}{2}$

$\frac{\pi^5}{4}$

Correct answer:

$\frac{\pi^5}{4}$

Explanation:

The radius of the circle is half the diameter, or $\frac{\pi^2}{2}$ .

Write the formula for the area of a circle.

$A = \pi r^2$

Substitute the radius.

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

The answer is: $\frac{\pi^5}{4}$

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Example Question #34 : Area Of A Circle

Determine the area of a circle with a radius of 16x .

Possible Answers:

$256\pi x^2$

$256\pi x$

$216\pi x^2$

32x^2

$32\pi x^2$

Correct answer:

$256\pi x^2$

Explanation:

Write the area of a circle.

$A =\pi r^2$

Substitute the radius into the equation.

$A =\pi (16x)^2=\pi (16x)(16x)$

The answer is: $256\pi x^2$

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Example Question #35 : Area Of A Circle

Let $\pi = 3.14$

Find the area of a circle with a diameter of 14cm.

Possible Answers:

$200.96\text{cm}^2$

$615.44\text{cm}^2$

$87.92\text{cm}^2$

$153.86\text{cm}^2$

$43.96\text{cm}^2$

Correct answer:

$153.86\text{cm}^2$

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 $\pi = 3.14$ . We know the diameter of the circle is 14cm. We also know the diameter is two times the radius. Therefore, the radius is 7cm. So, we can substitute. We get

$A = 3.14 \cdot (7\text{cm})^2$

$A = 3.14 \cdot 49\text{cm}^2$

$A = 153.86\text{cm}^2$

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Example Question #36 : Area Of A Circle

Find the area of a circle with a diameter of $10\pi$ .

Possible Answers:

$50\pi$

$25\pi ^2$

$25\pi ^3$

$100\pi^4$

Correct answer:

$25\pi ^3$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

The radius is half the diameter. Multiply the radius by one half.

$10\pi \cdot \frac{1}{2} = 5\pi$

Substitute the radius into the equation.

$A=\pi (5\pi)^2 = \pi (5\pi)(5\pi) = 25\pi ^3$

The answer is: $25\pi ^3$

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Example Question #37 : Area Of A Circle

Determine the area of a circle with a diameter of $\frac{5}{3}$ .

Possible Answers:

$\frac{25}{36}\pi$

$\frac{25}{18}\pi$

$\frac{25}{9}\pi$

$\frac{5}{18}\pi$

$\frac{100}{9}\pi$

Correct answer:

$\frac{25}{36}\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

The radius is half the diameter. Multiply the diameter by half.

$\frac{5}{3}\cdot \frac{1}{2} = \frac{5}{6}$

Substitute the radius into the equation.

$A=\pi (\frac{5}{6})^2= \pi (\frac{5}{6})(\frac{5}{6}) = \frac{25}{36}\pi$

The answer is: $\frac{25}{36}\pi$

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Example Question #131 : Circles

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

Possible Answers:

$24\pi$

144

$24\pi ^2$

$144\pi^2$

$144\pi$

Correct answer:

$144\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (12)^2 = \pi (144)$

The answer is: $144\pi$

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Example Question #31 : Area Of A Circle

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

Possible Answers:

$200\pi$

$20\pi$

$100\pi$

$50\pi$

$400\pi$

Correct answer:

$100\pi$

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 $2\pi$ .

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

r=10

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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Example Question #40 : Area Of A Circle

Find the area of a circle with a radius of $7\pi ^3$ .

Possible Answers:

$7\pi ^6$

$14\pi ^6$

$14\pi ^7$

$49 \pi ^6$

$49 \pi ^7$

Correct answer:

$49 \pi ^7$

Explanation:

Write the formula for the area of a circle.

$A = \pi r^2$

Substitute the radius into the formula.

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

The answer is: $49 \pi ^7$

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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 #31 : Area Of A Circle

Example Question #32 : Area Of A Circle

Example Question #33 : Area Of A Circle

Example Question #34 : Area Of A Circle

Example Question #35 : Area Of A Circle

Example Question #36 : Area Of A Circle

Example Question #37 : Area Of A Circle

Example Question #131 : Circles

Example Question #31 : Area Of A Circle

Example Question #40 : Area Of A Circle

All GED Math Resources

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