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GED Math : 2-Dimensional Geometry

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #41 : Circumference

Find the circumference of a circle if the radius is $5\pi$ $\displaystyle 5\pi$.

Possible Answers:

$10+2\pi ^2$ $\displaystyle 10+2\pi ^2$

$10\pi$ $\displaystyle 10\pi$

$10\pi^2$ $\displaystyle 10\pi^2$

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

$10+2\pi$ $\displaystyle 10+2\pi$

Correct answer:

$10\pi^2$ $\displaystyle 10\pi^2$

Explanation:

Write the formula for the circumference of a circle.

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

Substitute the radius.

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

The answer is: $10\pi^2$ $\displaystyle 10\pi^2$

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Example Question #42 : Circumference

Find the circumference of the circle with a diameter of $2\pi -3$ $\displaystyle 2\pi -3$.

Possible Answers:

$4\pi^2-12\pi+9$ $\displaystyle 4\pi^2-12\pi+9$

$2\pi ^2-3\pi$ $\displaystyle 2\pi ^2-3\pi$

$4\pi ^2-6\pi$ $\displaystyle 4\pi ^2-6\pi$

$2\pi ^2-3$ $\displaystyle 2\pi ^2-3$

$4\pi ^2-6$ $\displaystyle 4\pi ^2-6$

Correct answer:

$2\pi ^2-3\pi$ $\displaystyle 2\pi ^2-3\pi$

Explanation:

Write the formula for the circumference of the circle.

$C=2\pi r = \pi D$ $\displaystyle C=2\pi r = \pi D$

Substitute the diameter.

$C= \pi (2\pi-3) = 2\pi ^2-3\pi$ $\displaystyle C= \pi (2\pi-3) = 2\pi ^2-3\pi$

The answer is: $2\pi ^2-3\pi$ $\displaystyle 2\pi ^2-3\pi$

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Example Question #81 : Circles

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

Possible Answers:

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

$\frac{25}{6} \pi$ $\displaystyle \frac{25}{6} \pi$

$\frac{25}{3} \pi$ $\displaystyle \frac{25}{3} \pi$

$\frac{5}{6} \pi$ $\displaystyle \frac{5}{6} \pi$

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

Correct answer:

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

Explanation:

Write the formula for the circumference of the circle.

$C= 2\pi r = \pi D$ $\displaystyle C= 2\pi r = \pi D$

Substitute the diameter.

$C = \pi(\frac{5}{3})$ $\displaystyle C = \pi(\frac{5}{3})$

The answer is: $\frac{5}{3} \pi$ $\displaystyle \frac{5}{3} \pi$

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Example Question #81 : 2 Dimensional Geometry

You have a giant gong that has a diameter of 1.5 m $\displaystyle 1.5 m$. Find the circumference of the gong.

Possible Answers:

9.42m $\displaystyle 9.42m$

4.71m $\displaystyle 4.71m$

2.25m $\displaystyle 2.25m$

2.36 m $\displaystyle 2.36 m$

Correct answer:

4.71m $\displaystyle 4.71m$

Explanation:

You have a giant gong that has a diameter of 1.5 m $\displaystyle 1.5 m$. Find the circumference of the gong.

To find the circumference of a circle, simply use the following formula:

$Circ=2\pi r=d \pi$ $\displaystyle Circ=2\pi r=d \pi$

So, if we plug in our diameter, we get:

$C=\pi (1.5m)=4.71 m$ $\displaystyle C=\pi (1.5m)=4.71 m$

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Example Question #82 : 2 Dimensional Geometry

While doing your homework, you become distracted by the 3 holes on the margin of your paper. You estimate that the holes have a diameter of 2.5 cm. What is the circumference of the circles?

Possible Answers:

4.91 cm $\displaystyle 4.91 cm$

5cm $\displaystyle 5cm$

$\displaystyle 19.63 cm$

7.85cm $\displaystyle 7.85cm$

Correct answer:

7.85cm $\displaystyle 7.85cm$

Explanation:

While doing your homework, you become distracted by the 3 holes on the margin of your paper. You estimate that the holes have a diameter of 2.5 cm. What is the circumference of the circles?

To find circumference, use the following formula:

$C=2 \pi r$ $\displaystyle C=2 \pi r$

Now, we could find the radius and then plug it in, but if you are astute, you will see that the above formula is the same thing as:

$C= \pi d$ $\displaystyle C= \pi d$

Where d is the diameter.

So, we can plug in our diameter to find our answer:

$C= \pi (2.5cm)\approx 7.85cm$ $\displaystyle C= \pi (2.5cm)\approx 7.85cm$

So we can say our answer is 7.85 cm

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Example Question #83 : 2 Dimensional Geometry

Find the area of a circle that has a circumference of $26\pi$ $\displaystyle 26\pi$.

Possible Answers:

$13\pi$ $\displaystyle 13\pi$

$52\pi$ $\displaystyle 52\pi$

$169\pi$ $\displaystyle 169\pi$

$130\pi$ $\displaystyle 130\pi$

Correct answer:

$169\pi$ $\displaystyle 169\pi$

Explanation:

Recall how to find the circumference of a circle:

$\text{Circumference}=2\pi r$ $\displaystyle \text{Circumference}=2\pi r$, where $\displaystyle r$ is the radius.

Using the given circumference, solve for $\displaystyle r$.

$26\pi=2\pi r$ $\displaystyle 26\pi=2\pi r$

r=13 $\displaystyle r=13$

Now, recall how to find the area of a circle:

$\text{Area}=\pi r^2$ $\displaystyle \text{Area}=\pi r^2$

Plug in the radius to find the area.

$\text{Area}=\pi (13)^2=169\pi$ $\displaystyle \text{Area}=\pi (13)^2=169\pi$

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Example Question #44 : Circumference

Find the circumference of a circle with an area of $36\pi.$ $\displaystyle 36\pi.$

Possible Answers:

$36 \pi$ $\displaystyle 36 \pi$

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

$6 \pi$ $\displaystyle 6 \pi$

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

$18 \pi$ $\displaystyle 18 \pi$

Correct answer:

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

Explanation:

The problem is asking for us to solve for the circumference. However, the only provided information is the circle's area. In this kind of a problem, it's important think about how the provided information may relate to the information we need in order to solve for the problem.

The area of a circle is determined through the formula: $A=\pi r^2$ $\displaystyle A=\pi r^2$, where r is for radius.

The circumference of a circle is determined by the formula: $C= \pi d$ $\displaystyle C= \pi d$ where d is diameter. It can also be written as $C=2\pi r$ $\displaystyle C=2\pi r$ because the radius is half the length of the diameter.

We can now easily see that the two concepts, area and circumference, are related through the variable r. Therefore, if we can solve for r from the area, we can use that to then solve for circumference.

$36\pi = \pi r^2$ $\displaystyle 36\pi = \pi r^2$

$\frac{36 \pi}{\pi} = r^2$ $\displaystyle \frac{36 \pi}{\pi} = r^2$

36=r^2 $\displaystyle 36=r^2$

r=6 $\displaystyle r=6$

Now that we have solved for the radius, we can use this value to "plug and chug" into the circumference formula and solve.

$C= 2 \pi (6)$ $\displaystyle C= 2 \pi (6)$

$C= 12 \pi$ $\displaystyle C= 12 \pi$

Therefore, the circumference of the circle is $12\pi$ $\displaystyle 12\pi$.

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Example Question #45 : Circumference

What is the circumference of a circle with an area of $49\pi$ $\displaystyle 49\pi$?

Possible Answers:

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

$7 \pi$ $\displaystyle 7 \pi$

$13\pi$ $\displaystyle 13\pi$

$24.5 \pi$ $\displaystyle 24.5 \pi$

$14\pi$ $\displaystyle 14\pi$

Correct answer:

$14\pi$ $\displaystyle 14\pi$

Explanation:

The area of a circle is determined through the formula: $A=\pi r^2$ $\displaystyle A=\pi r^2$, where r is for radius.

$49\pi = \pi r^2$ $\displaystyle 49\pi = \pi r^2$

$\frac{49 \pi}{\pi} = r^2$ $\displaystyle \frac{49 \pi}{\pi} = r^2$

49=r^2 $\displaystyle 49=r^2$

r=7 $\displaystyle r=7$

Now that we have solved for the radius, we can use this value to "plug and chug" into the circumference formula and solve.

$C= 2 \pi (7)$ $\displaystyle C= 2 \pi (7)$

$C= 14 \pi$ $\displaystyle C= 14 \pi$

Therefore, the circumference of the circle is $14\pi$ $\displaystyle 14\pi$.

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Example Question #46 : Circumference

Find the circumference of a circle with an area of $196 \pi$ $\displaystyle 196 \pi$.

Possible Answers:

$14 \pi$ $\displaystyle 14 \pi$

$28\pi$ $\displaystyle 28\pi$

$46 \pi$ $\displaystyle 46 \pi$

$7 \pi$ $\displaystyle 7 \pi$

$23 \pi$ $\displaystyle 23 \pi$

Correct answer:

$28\pi$ $\displaystyle 28\pi$

Explanation:

The area of a circle is determined through the formula: $A=\pi r^2$ $\displaystyle A=\pi r^2$, where r is for radius.

$196\pi = \pi r^2$ $\displaystyle 196\pi = \pi r^2$

$\frac{196 \pi}{\pi} = r^2$ $\displaystyle \frac{196 \pi}{\pi} = r^2$

196=r^2 $\displaystyle 196=r^2$

r=14 $\displaystyle r=14$

Now that we have solved for the radius, we can use this value to "plug and chug" into the circumference formula and solve.

$C= 2 \pi (14)$ $\displaystyle C= 2 \pi (14)$

$C= 28 \pi$ $\displaystyle C= 28 \pi$

Therefore, the circumference of the circle is $28\pi$ $\displaystyle 28\pi$.

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Example Question #47 : Circumference

If a circle has a diameter of $\displaystyle 10$, what is its circumference?

Possible Answers:

33.7 $\displaystyle 33.7$

64.2 $\displaystyle 64.2$

31.4 $\displaystyle 31.4$

18.3 $\displaystyle 18.3$

27.9 $\displaystyle 27.9$

Correct answer:

31.4 $\displaystyle 31.4$

Explanation:

The problem is asking for us to solve for the circumference. However, the only provided information is the circle's diameter. In this kind of a problem, it's important think about how the provided information may relate to the information we need in order to solve for the problem.

The circumference of a circle is determined by the formula: $C=2\pi r$ $\displaystyle C=2\pi r$ where r is radius. It can also be written as $C= \pi d$ $\displaystyle C= \pi d$ because the diameter is twice the length of the radius.

We can now easily see that the two concepts, diameter and circumference, are related. Therefore, we just need to substitute the diameter value into the circumference formula to solve.

$C=10 \cdot \pi$ $\displaystyle C=10 \cdot \pi$

$C= 10 \pi$ $\displaystyle C= 10 \pi$

C=31.4 $\displaystyle C=31.4$

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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 #41 : Circumference

Example Question #42 : Circumference

Example Question #81 : Circles

Example Question #81 : 2 Dimensional Geometry

Example Question #82 : 2 Dimensional Geometry

Example Question #83 : 2 Dimensional Geometry

Example Question #44 : Circumference

Example Question #45 : Circumference

Example Question #46 : Circumference

Example Question #47 : Circumference

All GED Math Resources

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