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GED Math : Area of a Circle

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Example Questions

Example Question #116 : 2 Dimensional Geometry

Sector40

The figure above is a circle.

If the radius of the circle above is 9 in., what is the area of the sector? Round to the nearest hundredth.

Possible Answers:

6.28 in^2

in^2

21.53 in^2

19.55 in^2

28.27 in^2

Correct answer:

28.27 in^2

Explanation:

To find the area of a sector, you are looking for a percentage of the total circle's area. Thus, if the angle is degrees, you are looking for $\frac{40}{360}$ of a complete circle.

Given that the radius is in., you know that the area must be:

$A=\pi r^2 = \pi9^2=81\pi$

The area of the sector is:

$\frac{40}{360}*81\pi=28.27433388230785...$

28.27

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Example Question #117 : 2 Dimensional Geometry

Sector77

The figure above is a circle.

If the diameter of the circle above is 10 in., what is the area of the sector? Round to the nearest hundredth.

Possible Answers:

24.3 in^2

29.35 in^2

11.25 in^2

16.8 in^2

67.2 in^2

Correct answer:

16.8 in^2

Explanation:

To find the area of a sector, you are looking for a percentage of the total circle's area. Thus, if the angle is degrees, you are looking for $\frac{77}{360}$ of a complete circle.

Given that the diameter is in., you know that the radius is in. This means that the area must be:

$A=\pi r^2 = \pi5^2=25\pi$

The area of the sector is:

$\frac{77}{360}*25\pi=16.79879405044542...$

16.8

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Example Question #118 : 2 Dimensional Geometry

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

Possible Answers:

$8\pi \text{ in}^2$

$64\pi \text{ in}^2$

$16\pi \text{ in}^2$

$24\pi \text{ in}^2$

$32\pi \text{ in}^2$

Correct answer:

$64\pi \text{ in}^2$

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 8in. So, we can substitute. We get

$A = \pi \cdot (8\text{in})^2$

$A = \pi \cdot 64\text{in}^2$

$A = 64\pi \text{ in}^2$

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Example Question #119 : 2 Dimensional Geometry

Determine the area of a circle with an diameter of .

Possible Answers:

$800\pi$

$400\pi$

$100\pi$

$1600\pi$

$200\pi$

Correct answer:

$100\pi$

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: $100\pi$

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Example Question #121 : 2 Dimensional Geometry

Find the area of a circle with a diameter of $\frac{3}{2}$ .

Possible Answers:

$\frac{9}{4}\pi$

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

$\frac{9}{16}\pi$

$\frac{9}{2}\pi$

$9\pi$

Correct answer:

$\frac{9}{16}\pi$

Explanation:

Write the formula for the area of a circle.

$A = \pi r^2$

The radius is half the diameter.

Multiply the diameter by $\frac{1}{2}$ .

$\frac{1}{2} \times \frac{3}{2} = \frac{3}{4}$

Substitute the radius.

$A = \pi (\frac{3}{4})^2 = \pi (\frac{3}{4})(\frac{3}{4}) = \frac{9}{16}\pi$

The answer is: $\frac{9}{16}\pi$

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Example Question #122 : 2 Dimensional Geometry

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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

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Example Question #123 : 2 Dimensional Geometry

Circle 1

Give the area of the above circle.

Possible Answers:

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

$7 \pi$

$14 \pi$

$49 \pi$

Correct answer:

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

Explanation:

The area of a circle, given its radius , can be found using the formula

$A = \pi r^{2}$

The radius is half the diameter - that is, $r = \frac{d}{2}$ - so, substituting,

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

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

$A = \left ( \frac{d^{2}}{4} \right )\pi$

The diameter of the given circle is 7, so set d=7 in the above formula:

$A = \left ( \frac{7^{2}}{4} \right )\pi$

$A = \frac{49}{4} \pi$ ,

the correct area.

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Example Question #124 : 2 Dimensional Geometry

Let $\pi=3.14$ .

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

Possible Answers:

$452.16\text{in}^2$

$37.68\text{in}^2$

$56.52\text{in}^2$

$113.04\text{in}^2$

$40.80\text{in}^2$

Correct answer:

$113.04\text{in}^2$

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 also know the diameter is 12in. We know the diameter is two times the radius, so the radius is 6in. Now, we can substitute. We get

$A = 3.14 \cdot (6\text{in})^2$

$A = 3.14 \cdot 36\text{in}^2$

$A = 113.04\text{in}^2$

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Example Question #121 : Circles

What is the area of a circle with a circumference of $3\pi$ ?

Possible Answers:

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

$\frac{9}{4}\pi$

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

$9\pi$

$6\pi$

Correct answer:

$\frac{9}{4}\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

We will need to find the radius of the circle.

Write the formula for the circumference.

$C=2\pi r$

Substitute the circumference.

$3\pi=2\pi r$

Divide by $2\pi$ on both sides.

$\frac{3\pi}{2\pi }=\frac{2\pi r}{2\pi }$

The radius is: $\frac{3}{2}$

Substitute this into the area formula.

$A=\pi (\frac{3}{2})^2 = \frac{9}{4}\pi$

The answer is: $\frac{9}{4}\pi$

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Example Question #126 : 2 Dimensional Geometry

Find the area of the circle with radius of 9x^3 .

Possible Answers:

$81\pi x^9$

$81\pi x^6$

$81\pi^2 x^6$

9x^6

$81\pi^2 x^9$

Correct answer:

$81\pi x^6$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (9x^3)^2=\pi (9x^3)(9x^3) = 81\pi x^6$

The answer is: $81\pi x^6$

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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 #116 : 2 Dimensional Geometry

Example Question #117 : 2 Dimensional Geometry

Example Question #118 : 2 Dimensional Geometry

Example Question #119 : 2 Dimensional Geometry

Example Question #121 : 2 Dimensional Geometry

Example Question #122 : 2 Dimensional Geometry

Example Question #123 : 2 Dimensional Geometry

Example Question #124 : 2 Dimensional Geometry

Example Question #121 : Circles

Example Question #126 : 2 Dimensional Geometry

All GED Math Resources

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