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GED Math : 2-Dimensional Geometry

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Example Questions

Example Question #111 : 2 Dimensional Geometry

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

Possible Answers:

$30\pi$ $\displaystyle 30\pi$

$60\pi$ $\displaystyle 60\pi$

$250\pi$ $\displaystyle 250\pi$

$125\pi$ $\displaystyle 125\pi$

$225\pi$ $\displaystyle 225\pi$

Correct answer:

$225\pi$ $\displaystyle 225\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$ $\displaystyle A=\pi r^2$

Substitute the radius into the equation.

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

The answer is: $225\pi$ $\displaystyle 225\pi$

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Example Question #112 : 2 Dimensional Geometry

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

Possible Answers:

$10\pi ^4$ $\displaystyle 10\pi ^4$

$20\pi ^3$ $\displaystyle 20\pi ^3$

$10\pi^5$ $\displaystyle 10\pi^5$

$100\pi ^4$ $\displaystyle 100\pi ^4$

$100\pi ^5$ $\displaystyle 100\pi ^5$

Correct answer:

$100\pi ^5$ $\displaystyle 100\pi ^5$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$ $\displaystyle A=\pi r^2$

Substitute the radius into the equation.

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

The answer is: $100\pi ^5$ $\displaystyle 100\pi ^5$

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Example Question #113 : 2 Dimensional Geometry

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

Possible Answers:

$144\pi$ $\displaystyle 144\pi$

$2\pi$ $\displaystyle 2\pi$

$\pi$ $\displaystyle \pi$

$12\pi$ $\displaystyle 12\pi$

$24\pi$ $\displaystyle 24\pi$

Correct answer:

$\pi$ $\displaystyle \pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$ $\displaystyle A=\pi r^2$

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.

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

The answer is: $\pi$ $\displaystyle \pi$

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Example Question #114 : 2 Dimensional Geometry

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

$A = \pi \cdot r^2$ $\displaystyle A = \pi \cdot r^2$

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

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

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

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

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Example Question #115 : 2 Dimensional Geometry

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

$A = \pi \cdot r^2$ $\displaystyle A = \pi \cdot r^2$

where r is the radius of the circle.

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

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

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

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

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Example Question #116 : 2 Dimensional Geometry

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

Possible Answers:

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

$25\pi$ $\displaystyle 25\pi$

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

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

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

Correct answer:

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

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.

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

Write the formula for the area of a circle.

$A=\pi r^2$ $\displaystyle A=\pi r^2$

The radius is half the diameter.

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

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

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

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Example Question #117 : 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:

21.53 $\displaystyle 21.53$ in^2 $\displaystyle in^2$

6.28 $\displaystyle 6.28$ in^2 $\displaystyle in^2$

$\displaystyle 9$ in^2 $\displaystyle in^2$

28.27 $\displaystyle 28.27$ in^2 $\displaystyle in^2$

19.55 $\displaystyle 19.55$ in^2 $\displaystyle in^2$

Correct answer:

28.27 $\displaystyle 28.27$ in^2 $\displaystyle in^2$

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 $\displaystyle 40$ degrees, you are looking for $\frac{40}{360}$ $\displaystyle \frac{40}{360}$ of a complete circle.

Given that the radius is $\displaystyle 9$ in., you know that the area must be:

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

The area of the sector is:

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

28.27 $\displaystyle 28.27$

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Example Question #118 : 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:

67.2 $\displaystyle 67.2$ in^2 $\displaystyle in^2$

29.35 $\displaystyle 29.35$ in^2 $\displaystyle in^2$

24.3 $\displaystyle 24.3$ in^2 $\displaystyle in^2$

16.8 $\displaystyle 16.8$ in^2 $\displaystyle in^2$

11.25 $\displaystyle 11.25$ in^2 $\displaystyle in^2$

Correct answer:

16.8 $\displaystyle 16.8$ in^2 $\displaystyle in^2$

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 $\displaystyle 77$ degrees, you are looking for $\frac{77}{360}$ $\displaystyle \frac{77}{360}$ of a complete circle.

Given that the diameter is $\displaystyle 10$ in., you know that the radius is $\displaystyle 5$ in. This means that the area must be:

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

The area of the sector is:

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

16.8 $\displaystyle 16.8$

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Example Question #119 : 2 Dimensional Geometry

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

$A = \pi \cdot r^2$ $\displaystyle A = \pi \cdot r^2$

where r is the radius of the circle.

Now, we know the radius of the circle is 8in. So, we can substitute. We get

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

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

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

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Example Question #120 : 2 Dimensional Geometry

Determine the area of a circle with an diameter of $\displaystyle 20$ .

Possible Answers:

$400\pi$ $\displaystyle 400\pi$

$1600\pi$ $\displaystyle 1600\pi$

$100\pi$ $\displaystyle 100\pi$

$200\pi$ $\displaystyle 200\pi$

$800\pi$ $\displaystyle 800\pi$

Correct answer:

$100\pi$ $\displaystyle 100\pi$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$ $\displaystyle A=\pi r^2$

The radius is half the diameter.

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

The answer is: $100\pi$ $\displaystyle 100\pi$

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GED Math : 2-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #111 : 2 Dimensional Geometry

Example Question #112 : 2 Dimensional Geometry

Example Question #113 : 2 Dimensional Geometry

Example Question #114 : 2 Dimensional Geometry

Example Question #115 : 2 Dimensional Geometry

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 #120 : 2 Dimensional Geometry

All GED Math Resources

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