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GED Math : 2-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

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

Example Questions

Example Question #71 : Geometry And Graphs

Determine the circumference of the circle with a radius of $2\pi^3$ .

Possible Answers:

$16\pi^4$

$4\pi^4$

$8\pi^4$

$16\pi^3$

$4\pi^3$

Correct answer:

$4\pi^4$

Explanation:

Write the formula for the circumference of a circle.

$C= 2\pi r$

Substitute the radius.

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

The answer is: $4\pi^4$

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Example Question #32 : Circumference

Determine the circumference of a circle with an area of .

Possible Answers:

$6\sqrt{\pi}$

$3\sqrt{2\pi}$

$18\pi$

$2\sqrt{\pi}$

$6\sqrt{2\pi}$

Correct answer:

$6\sqrt{\pi}$

Explanation:

Write the formula for the circumference and area of the circle.

$C=2\pi r$

$A=\pi r^2$

Given the area, we will need to find the radius, which can be used to find the circumference. Substitute the area into the area equation.

$9=\pi r^2$

Solve for .

$\frac{9}{\pi }=\frac{\pi r^2}{\pi }$

$\frac{9}{\pi }=r^2$

Square root both sides.

$\sqrt{\frac{9}{\pi }}=\sqrt{r^2}$

$r=\sqrt{\frac{9}{\pi }}= \frac{3}{\sqrt{\pi}}$

Substitute this back into the circumference equation.

$C=2\pi r = 2\pi \frac{3}{\sqrt{\pi}} = \frac{6\pi}{\sqrt{\pi}} = \frac{6 \sqrt{\pi} \cdot \sqrt{\pi}}{\sqrt{\pi}}$

The answer is: $6\sqrt{\pi}$

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Example Question #71 : Geometry And Graphs

Find the circumference with a radius of 50.

Possible Answers:

$250\pi$

$50\pi$

$100 \pi$

$2500\pi$

$200\pi$

Correct answer:

$100 \pi$

Explanation:

Write the formula to find the circumference of a circle.

$C=2\pi r$

Substitute the radius into the equation.

$C=2\pi (50)$

The circumference is: $100 \pi$

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Example Question #72 : Circles

Find the circumference of a circle with the diameter of 2x-5 .

Possible Answers:

$\pi x -\frac{5}{2}$

$2\pi x -5\pi$

$2\pi x -5$

$\pi x -5$

$\pi x -\frac{5}{2}\pi$

Correct answer:

$2\pi x -5\pi$

Explanation:

Write the formula for the circumference of a circle.

$C=\pi D$

Substitute the diameter.

$C=\pi (2x-5) = 2\pi x -5\pi$

The answer is: $2\pi x -5\pi$

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Example Question #35 : Circumference

A circle has a radius of 10cm. Find the circumference.

Possible Answers:

$20\pi \text{ cm}$

$100\pi \text{ cm}$

$10\pi \text{ cm}$

$50\pi \text{ cm}$

$15\pi \text{ cm}$

Correct answer:

$20\pi \text{ cm}$

Explanation:

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

$C = 2 \pi r$

where r is the radius of the circle.

Now, we know the radius of the circle is 10cm. So, we will substitute. We get

$C = 2 \cdot \pi \cdot 10\text{cm}$

$C = 2 \cdot 10\text{cm} \cdot \pi$

$C = 20\text{cm} \cdot \pi$

$C = 20\pi \text{ cm}$

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Example Question #36 : Circumference

Let $\pi = 3.14$ .

Find the circumference of a circle with a diameter of 8in.

Possible Answers:

$12.56\text{in}$

$25.12\text{in}$

$200.96\text{in}$

$50.24\text{in}$

$6.28\text{in}$

Correct answer:

$25.12\text{in}$

Explanation:

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

$C = \pi d$

where d is the diameter of the circle.

Now, we know $\pi = 3.14$ . We know the diameter of the circle is 8in. So, we substitute. We get

$C = 3.14 \cdot 8\text{in}$

$C = 25.12\text{in}$

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Example Question #37 : Circumference

Determine the circumference of the circle with a radius of 6x-3 .

Possible Answers:

$36x\pi x^2 -36x \pi -9 \pi$

$12\pi x-3$

$36\pi x^2-9\pi$

$12\pi x-3\pi$

$12\pi x-6\pi$

Correct answer:

$12\pi x-6\pi$

Explanation:

Write the formula for the circumference of the circle.

$C=2\pi r$

Substitute the radius.

$C=2\pi (6x-3) = 12\pi x-6\pi$

The answer is: $12\pi x-6\pi$

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Example Question #72 : Geometry And Graphs

Let $\pi = 3.14$

Find the circumference of a circle with a diameter of 20in.

Possible Answers:

$314\text{in}^2$

$31.4\text{in}^2$

$62.8\text{in}^2$

$47.1\text{in}^2$

$125.6\text{in}^2$

Correct answer:

$62.8\text{in}^2$

Explanation:

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

$C = \pi d$

where d is the diameter of the circle.

Now, we know $\pi = 3.14$ . We know the diameter of the circle is 20in. So, we can substitute. We get

$C = 3.14 \cdot 20\text{in}$

$C = 62.8\text{in}$

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Example Question #72 : Circles

Find the circumference of a circle with a radius of $3\pi +2$ .

Possible Answers:

$10\pi ^2$

$10\pi$

$7\pi$

$6\pi + 4$

$6\pi^2 + 4\pi$

Correct answer:

$6\pi^2 + 4\pi$

Explanation:

Write the formula for the circumference of the circle.

$C=2\pi r$

Substitute the radius.

$C=2\pi (3\pi +2) =6\pi^2 + 4\pi$

The answer is: $6\pi^2 + 4\pi$

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Example Question #40 : Circumference

Find the circumference of a circle with a diameter of $6\pi^5$ .

Possible Answers:

$6\pi ^5$

$12\pi ^5$

$12\pi ^6$

$6\pi ^6$

$6\pi ^3$

Correct answer:

$6\pi ^6$

Explanation:

Write the formula for the circumference of the circle.

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

Substitute the diameter.

$C= \pi (6\pi ^5) = 6\pi ^6$

The answer is: $6\pi ^6$

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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 #71 : Geometry And Graphs

Example Question #32 : Circumference

Example Question #71 : Geometry And Graphs

Example Question #72 : Circles

Example Question #35 : Circumference

Example Question #36 : Circumference

Example Question #37 : Circumference

Example Question #72 : Geometry And Graphs

Example Question #72 : Circles

Example Question #40 : Circumference

All GED Math Resources

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