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GED Math : Geometry and Graphs

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

Example Questions

Example Question #62 : 3 Dimensional Geometry

Find the volume of a cylinder with a base diameter of 6, and a height of 7.

Possible Answers:

$126\pi$ $\displaystyle 126\pi$

$63\pi$ $\displaystyle 63\pi$

$84\pi$ $\displaystyle 84\pi$

$21\pi$ $\displaystyle 21\pi$

$42\pi$ $\displaystyle 42\pi$

Correct answer:

$63\pi$ $\displaystyle 63\pi$

Explanation:

Write the formula for the area of a cylinder.

$V=\pi r^2 h$ $\displaystyle V=\pi r^2 h$

The radius is half the diameter, of three.

Substitute the known dimensions into the formula.

$V=\pi (3)^2 7 = \pi (9) 7 = 63\pi$ $\displaystyle V=\pi (3)^2 7 = \pi (9) 7 = 63\pi$

The answer is: $63\pi$ $\displaystyle 63\pi$

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Example Question #621 : Geometry And Graphs

Find the volume of a cylinder with a radius of 8, and a height of 20.

Possible Answers:

$1280\pi$ $\displaystyle 1280\pi$

$320\pi$ $\displaystyle 320\pi$

$120\pi$ $\displaystyle 120\pi$

$640\pi$ $\displaystyle 640\pi$

$\frac{1280}{3}\pi$ $\displaystyle \frac{1280}{3}\pi$

Correct answer:

$1280\pi$ $\displaystyle 1280\pi$

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2h$ $\displaystyle V=\pi r^2h$

Substitute the radius and height into the equation.

$V=\pi( 8)^2(20)= \pi( 64)(20)$ $\displaystyle V=\pi( 8)^2(20)= \pi( 64)(20)$

The answer is: $1280\pi$ $\displaystyle 1280\pi$

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Example Question #71 : 3 Dimensional Geometry

Let $\pi = 3.14$ $\displaystyle \pi = 3.14$

If a cylinder has a height of 7in and a radius of 4in, find the volume.

Possible Answers:

$87.92\text{in}^3$ $\displaystyle 87.92\text{in}^3$

$351.68\text{in}^3$ $\displaystyle 351.68\text{in}^3$

$615.44\text{in}^3$ $\displaystyle 615.44\text{in}^3$

$175.84\text{in}^3$ $\displaystyle 175.84\text{in}^3$

$703.36\text{in}^3$ $\displaystyle 703.36\text{in}^3$

Correct answer:

$351.68\text{in}^3$ $\displaystyle 351.68\text{in}^3$

Explanation:

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$ $\displaystyle V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

We know $\pi=3.14$ $\displaystyle \pi=3.14$.

We know the radius of the cylinder is 4in.

We know the height of the cylinder is 7in.

Now, we can substitute. We get

$V = 3.14 \cdot (4\text{in})^2 \cdot 7\text{in}$ $\displaystyle V = 3.14 \cdot (4\text{in})^2 \cdot 7\text{in}$

$V = 3.14 \cdot 16\text{in}^2 \cdot 7\text{in}$ $\displaystyle V = 3.14 \cdot 16\text{in}^2 \cdot 7\text{in}$

$V = 3.14 \cdot 112\text{in}^3$ $\displaystyle V = 3.14 \cdot 112\text{in}^3$

$V = 351.68\text{in}^3$ $\displaystyle V = 351.68\text{in}^3$

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Example Question #22 : Volume Of A Cylinder

Find the volume of a cylinder with a base area of 15, and a height of 10.

Possible Answers:

2250 $\displaystyle 2250$

$150\pi$ $\displaystyle 150\pi$

$2250\pi$ $\displaystyle 2250\pi$

$\frac{75}{4}\pi$ $\displaystyle \frac{75}{4}\pi$

150 $\displaystyle 150$

Correct answer:

150 $\displaystyle 150$

Explanation:

Write the volume formula for the cylinder. The area of the base is a circle or $\pi r^2$ $\displaystyle \pi r^2$.

$V =\pi r^2h =Bh$ $\displaystyle V =\pi r^2h =Bh$

Substitute the base and height.

$\displaystyle V =(15)(10) = 150$

The volume is: 150 $\displaystyle 150$

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Example Question #22 : Volume Of A Cylinder

Let $\pi = 3.14$ $\displaystyle \pi = 3.14$.

Find the volume of a cylinder with a radius of 4cm and a height of 6cm.

Possible Answers:

$452.16\text{cm}^3$ $\displaystyle 452.16\text{cm}^3$

$87.92\text{cm}^3$ $\displaystyle 87.92\text{cm}^3$

$150.72\text{cm}^3$ $\displaystyle 150.72\text{cm}^3$

$301.44\text{cm}^3$ $\displaystyle 301.44\text{cm}^3$

$75.36\text{cm}^3$ $\displaystyle 75.36\text{cm}^3$

Correct answer:

$301.44\text{cm}^3$ $\displaystyle 301.44\text{cm}^3$

Explanation:

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$ $\displaystyle V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

Now, we know $\pi = 3.14$ $\displaystyle \pi = 3.14$. We know the radius of the cylinder is 4cm. We know the height of the cylinder is 6cm. So, we substitute. We get

$V = 3.14 \cdot (4\text{cm})^2 \cdot 6\text{cm}$ $\displaystyle V = 3.14 \cdot (4\text{cm})^2 \cdot 6\text{cm}$

$V = 3.14 \cdot 16\text{cm}^2 \cdot 6\text{cm}$ $\displaystyle V = 3.14 \cdot 16\text{cm}^2 \cdot 6\text{cm}$

$V = 3.14 \cdot 96\text{cm}^3$ $\displaystyle V = 3.14 \cdot 96\text{cm}^3$

$V = 301.44\text{cm}^3$ $\displaystyle V = 301.44\text{cm}^3$

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Example Question #622 : Geometry And Graphs

Find the volume of a cylinder with a radius of 10, and a height of 20.

Possible Answers:

$2000\pi$ $\displaystyle 2000\pi$

$\frac{2000\pi}{3}$ $\displaystyle \frac{2000\pi}{3}$

$4000\pi$ $\displaystyle 4000\pi$

$\frac{200\pi}{3}$ $\displaystyle \frac{200\pi}{3}$

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

Correct answer:

$2000\pi$ $\displaystyle 2000\pi$

Explanation:

Write the formula for the volume of a cylinder.

$V= \pi r^2 h$ $\displaystyle V= \pi r^2 h$

Substitute the radius and height.

$V= \pi (10)^2 (20) = \pi (100) (20)$ $\displaystyle V= \pi (10)^2 (20) = \pi (100) (20)$

The answer is: $2000\pi$ $\displaystyle 2000\pi$

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Example Question #623 : Geometry And Graphs

Find the volume of a cylinder with a radius of 5 and a height of 12.

Possible Answers:

$300 \pi$ $\displaystyle 300 \pi$

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

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

$120\pi$ $\displaystyle 120\pi$

$90\pi$ $\displaystyle 90\pi$

Correct answer:

$300 \pi$ $\displaystyle 300 \pi$

Explanation:

Write the formula for the volume of a cylinder.

$V= \pi r^2 h$ $\displaystyle V= \pi r^2 h$

Substitute the dimensions.

$V= \pi (5)^2 (12) = \pi (25) (12 )= 300 \pi$ $\displaystyle V= \pi (5)^2 (12) = \pi (25) (12 )= 300 \pi$

The answer is: $300 \pi$ $\displaystyle 300 \pi$

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Example Question #622 : Geometry And Graphs

Determine the volume of a cylinder with a radius of $3\pi^4$ $\displaystyle 3\pi^4$ and a height of $\pi$ $\displaystyle \pi$.

Possible Answers:

$3\pi ^{20}$ $\displaystyle 3\pi ^{20}$

$3\pi ^{10}$ $\displaystyle 3\pi ^{10}$

$9\pi ^{10}$ $\displaystyle 9\pi ^{10}$

$9\pi ^{20}$ $\displaystyle 9\pi ^{20}$

$9\pi ^6$ $\displaystyle 9\pi ^6$

Correct answer:

$9\pi ^{10}$ $\displaystyle 9\pi ^{10}$

Explanation:

Write the formula for the volume of a cylinder.

$V=\pi r^2 h$ $\displaystyle V=\pi r^2 h$

Substitute the radius and height.

$V=\pi (3\pi^4)^2 (\pi)$ $\displaystyle V=\pi (3\pi^4)^2 (\pi)$

Simplify the terms.

$V=\pi (3\pi^4)^2 (\pi) = \pi (3\pi^4)(3\pi^4) (\pi)$ $\displaystyle V=\pi (3\pi^4)^2 (\pi) = \pi (3\pi^4)(3\pi^4) (\pi)$

The answer is: $9\pi ^{10}$ $\displaystyle 9\pi ^{10}$

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Example Question #31 : Volume Of A Cylinder

Determine the volume of a cylinder with a base area of 8, and a height of 6.

Possible Answers:

$384\pi$ $\displaystyle 384\pi$

$\displaystyle 48$

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

$48\pi$ $\displaystyle 48\pi$

384 $\displaystyle 384$

Correct answer:

$\displaystyle 48$

Explanation:

Write the volume for a cylinder.

$V =\pi r^2h$ $\displaystyle V =\pi r^2h$

The base of a cylinder is a circle, and the area of the base is: $\pi r^2$ $\displaystyle \pi r^2$

We can substitute the area and the height.

$V =\pi r^2h= Bh = 8(6) = 48$ $\displaystyle V =\pi r^2h= Bh = 8(6) = 48$

The answer is: $\displaystyle 48$

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Example Question #75 : 3 Dimensional Geometry

Find the volume of a cylinder with a radius of 7in and a height of 4in.

Possible Answers:

$112\pi \text{ in}^3$ $\displaystyle 112\pi \text{ in}^3$

$224\pi \text{ in}^3$ $\displaystyle 224\pi \text{ in}^3$

$192\pi \text{ in}^3$ $\displaystyle 192\pi \text{ in}^3$

$448\pi \text{ in}^3$ $\displaystyle 448\pi \text{ in}^3$

$196\pi \text{ in}^3$ $\displaystyle 196\pi \text{ in}^3$

Correct answer:

$196\pi \text{ in}^3$ $\displaystyle 196\pi \text{ in}^3$

Explanation:

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$ $\displaystyle V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

Now, we know the radius is 7in. We know the height is 4in. So, we substitute. We get

$V = \pi \cdot (7\text{in})^2 \cdot 3\text{in}$ $\displaystyle V = \pi \cdot (7\text{in})^2 \cdot 3\text{in}$

$V = \pi \cdot 49\text{in}^2 \cdot 4\text{in}$ $\displaystyle V = \pi \cdot 49\text{in}^2 \cdot 4\text{in}$

$V = \pi \cdot 196\text{in}^3$ $\displaystyle V = \pi \cdot 196\text{in}^3$

$V = 196\pi \text{ in}^3$ $\displaystyle V = 196\pi \text{ in}^3$

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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 #62 : 3 Dimensional Geometry

Example Question #621 : Geometry And Graphs

Example Question #71 : 3 Dimensional Geometry

Example Question #22 : Volume Of A Cylinder

Example Question #22 : Volume Of A Cylinder

Example Question #622 : Geometry And Graphs

Example Question #623 : Geometry And Graphs

Example Question #622 : Geometry And Graphs

Example Question #31 : Volume Of A Cylinder

Example Question #75 : 3 Dimensional Geometry

All GED Math Resources

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