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GED Math : Geometry and Graphs

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Example Questions

Example Question #1 : Geometry And Graphs

What is the diameter of a circle with radius of 10 inches?

Possible Answers:

Correct answer:

Explanation:

The diameter is twice the radius:

D=2(10)

D=20

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Example Question #1 : Circles

What is the radius of a circle that has a circumference of $36\pi$ ?

Possible Answers:

Correct answer:

Explanation:

The equation for circumference of a circle is as follows:

$C=2 \pi r$

Plug in the given values and solve for the radius:

$36\pi=2\pi r$

Now we divide each side by $2\pi$ :

18=r

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Example Question #3 : Geometry And Graphs

Find the diameter of a circle that has a circumference of $25\pi$ ?

Possible Answers:

12.5

Correct answer:

Explanation:

We know the equation for the circumference of a circle is $C=2\pi r$ . We also know that the the diameter is the twice the radius, so we can write $C=D\pi$ .

Plug in the given values and solve:

$25\pi=D\pi$

25=D

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Example Question #4 : Geometry And Graphs

What is the diameter of a circle with a radius of 9?

Possible Answers:

Correct answer:

Explanation:

The diameter of a circle is twice the radius:

D=2r

Plug in the radius value:

D=2(9)

D=18

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Example Question #5 : Geometry And Graphs

What is the radius of a circle given the diameter is 22?

Possible Answers:

Correct answer:

Explanation:

The radius is half of the diameter, or 11.

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Example Question #2 : 2 Dimensional Geometry

What is the diameter of a circle with an area of $144\pi$ ?

Possible Answers:

$24\pi$

$12\pi$

Correct answer:

Explanation:

In order to solve this question, start by finding the radius. Recall that the area of a circle is computed as:

$A=\pi r^2$

For our data, this is:

$144\pi = \pi r^2$

Solving for , we get:

144=r^2 or r=12

Now, recall that the diameter is double the radius. Thus, it is .

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Example Question #3 : 2 Dimensional Geometry

What is the radius of a circle with a circumference of ?

Possible Answers:

$17\pi$

Cannot be computed from the information provided

$\frac{17}{\pi}$

$\frac{34}{\pi}$

$34\pi$

Correct answer:

$\frac{17}{\pi}$

Explanation:

Recall that the circumference formula is:

$C=2\pi r$

Now, for your data, this gives you:

$17=\pi r$

You need to be careful, for some students get confused when they have to divide by $\pi$ . However, just treat it like any other number or variable. This means that you can solve for and get:

$r=\frac{17}{\pi}$

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Example Question #2 : Geometry And Graphs

What is the diameter of a circle given the area of 30?

Possible Answers:

$15\sqrt{\frac{4}{\pi}}$

$5\sqrt{\frac{3}{\pi}}$

$\sqrt{\frac{30}{\pi}}$

$2\sqrt{\frac{30}{\pi}}$

$2\sqrt{\frac{15}{\pi}}$

Correct answer:

$2\sqrt{\frac{30}{\pi}}$

Explanation:

Write the area formula of a circle.

$A=\pi r^2$

Substitute the area.

$30=\pi r^2$

Divide by pi on both sides.

$\frac{30}{\pi}=\frac{\pi r^2}{\pi}$

$r^2 = \frac{30}{\pi}$

Square root both sides.

$\sqrt{r^2} =\sqrt{ \frac{30}{\pi}}$

$r=\sqrt{ \frac{30}{\pi}}$

The radius is: $\sqrt{\frac{30}{\pi}}$

The diameter is double the radius.

The answer is: $2\sqrt{\frac{30}{\pi}}$

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Example Question #2 : Radius And Diameter

What is the diameter of a circle if the area is $14\pi$ ?

Possible Answers:

$2\sqrt{7}$

$2\sqrt{14}$

$\sqrt{14}$

$7\sqrt2$

Correct answer:

$2\sqrt{14}$

Explanation:

Write the formula for the area of a circle.

$A=\pi r^2$

Substitute the area into the equation.

$14\pi=\pi r^2$

Divide by pi on both sides.

$\frac{14\pi}{\pi}=\frac{\pi r^2}{\pi}$

r^2 = 14

$r=\sqrt{14}$

The diameter is twice the radius.

The answer is: $2\sqrt{14}$

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Example Question #1 : 2 Dimensional Geometry

If the diameter of a circle is 12 feet, what is the radius in yards?

Possible Answers:

Correct answer:

Explanation:

There are three feet in one yard.

Using dimensional analysis, we can determine the given diameter in yards first.

$12 \textup{ ft}(\frac{1 \textup{ yd}}{3 \textup{ ft}}) = 4 \textup{ yds}$

The radius is half the diameter.

The answer is: $2 \textup{ yds}$

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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Geometry And Graphs

Example Question #1 : Circles

Example Question #3 : Geometry And Graphs

Example Question #4 : Geometry And Graphs

Example Question #5 : Geometry And Graphs

Example Question #2 : 2 Dimensional Geometry

Example Question #3 : 2 Dimensional Geometry

Example Question #2 : Geometry And Graphs

Example Question #2 : Radius And Diameter

Example Question #1 : 2 Dimensional Geometry

All GED Math Resources

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