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GED Math : GED Math

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

Example Questions

Example Question #41 : Volume Of A Cylinder

A cylinder has a height of and a circumference of $z\pi$ . What is its volume?

Possible Answers:

$\frac{1}{2}z^2x\pi$

$\frac{1}{2}zx\pi$

$\frac{1}{4}z^3x\pi$

$\frac{1}{8}z^2x^3\pi$

$z^2x^2\pi$

Correct answer:

$\frac{1}{2}z^2x\pi$

Explanation:

The volume of a cylinder can be solved for very simply. Just make sure you have the formula for volume handy!

The formula for the volume of a cylinder is: $V = \pi r^2h$ , where r is radius and h is the height. It's helpful to remember that volume will provide a value in units cubed, where area or surface area will provide a value in units squared. This minor detail confuses many students.

Looking at the problem, we have been provided with the height and the circumference. This problem provides a slight curve ball in that we indirectly have been given the radius, so we need to do some detective work. What is the relationship between radius and circumference? The circumference is $\pi$ times the diameter. This can be mathematically defined as: $C=\pi d$ .

We may solve for the diameter by using this formula. Keep in mind we are solving for d.

$z\pi = \pi d$

Now divide both sides by $\pi$ to solve for d.

$\frac{z\pi}{\pi} = \frac{d{\color{Red} \pi}}{{\color{Red} \pi}}$

d=z

We're almost there. Now we need to solve for the radius. The diameter is twice the radius. Or in math speak: d = 2r . This means we can solve for our radius by taking half of the diameter. Therefore, the radius is $\frac{1}{2}z$ .

Now we are ready to "plug and chug" to get our final answer.

$V = \pi \times (\frac{1}{2}z)^{2} \times 2x$

$V = \pi \times \frac{1}{4}z^2 \times 2x$

$V= \pi \times \frac{2}{4}z^2x$

$V=\frac{1}{2}z^2x\pi$

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Example Question #1611 : Ged Math

Pyramid_1

The above square pyramid has volume 100. Evaluate to the nearest tenth.

Possible Answers:

14.1

5.8

17.3

6.7

Correct answer:

6.7

Explanation:

The volume of a square pyramid with base of area and with height is

$V = \frac{1}{3} Bh$ .

The base, being a square of sidelength , has area $x^{2}$ . The height is . Therefore, setting $V = 100, B = x^{2}, h = x$ , we solve for in the equation

$\frac{1}{3} x^{2} \cdot x = 100$

$\frac{1}{3} x^{3} = 100$

$x^{3} = 300$

$x = \sqrt[3]{300} \approx 6.7$

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Example Question #92 : 3 Dimensional Geometry

A square pyramid whose base has sidelength has volume $2A^{3}$ . What is the ratio of the height of the pyramid to the sidelength of its base?

Possible Answers:

3:1

4:1

6:1

8:1

Correct answer:

6:1

Explanation:

Since the correct answer is independent of the value of , for simplicity's sake, assume that A = 1 .

The volume of a square pyramid with base of area and with height is

$V = \frac{1}{3} Bh$ .

The base, being a square of sidelength 1, has area 1. In the volume formula, we set B = 1 and $V = 2 A^{3} = 2 \cdot 1^{3} = 2$ , and solve for :

$\frac{1}{3} \cdot 1 \cdot h = 2$

$\frac{1}{3} h = 2$

$3 \cdot \frac{1}{3} h =3 \cdot 2$

h = 6

This means that the height-to-sidelength ratio h:A is equal to 6:1 , which is the correct response.

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Example Question #1612 : Ged Math

Suppose a triangular pyramid has base area of 10, and a height of 6. What is the volume?

Possible Answers:

120

Correct answer:

Explanation:

Write the formula for the volume of a pyramid.

$V= \frac{B\times h}{3}$

Substitute the known base area and the height into the formula.

$V= \frac{10\times 6}{3} = \frac{60}{3} = 20$

The answer is:

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Example Question #93 : 3 Dimensional Geometry

If the base of a pyramid is a square, with a length of 5, and the height of the pyramid is 9, what must be the volume?

Possible Answers:

225

150

Correct answer:

Explanation:

Write the formula for the volume of pyramid.

$V=\frac{Bh}{3}$

The base area of a square is s^2 .

Substituting the side length:

B=s^2 = 5^2 = 25

Substitute the base area and the height.

$V=\frac{25\times 9}{3} = 25\times 3 = 75$

The answer is:

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Example Question #1613 : Ged Math

Suppose the base area of a pyramid is 24, and the height is 10. What must the volume be?

Possible Answers:

$\textup{There is not enough information.}$

720

160

240

Correct answer:

Explanation:

Write formula for a pyramid.

$V=\frac{(LW)H}{3} = \frac{BH}{3}$

Substitute the base and height.

$V = \frac{24\times 10}{3} = 8\times 10 = 80$

The answer is:

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Example Question #2 : Volume Of A Pyramid

Find the volume of a pyramid with a square base area of and a height of .

Possible Answers:

Correct answer:

Explanation:

Write the formula of the volume of a pyramid.

$V = \frac{LWH}{3}$

The base area is represented by . This means the volume is:

$V = \frac{LWH}{3} =\frac{BH}{3}$

Substitute the base and height.

$V=\frac{6(10)}{3} = 20$

The answer is:

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Example Question #4 : Volume Of A Pyramid

Find the volume of a square pyramid with a base area of 12 and a height of 4.

Possible Answers:

576

192

$\textup{The volume cannot be determined.}$

Correct answer:

Explanation:

Write the formula for the volume of a pyramid.

$V = \frac{LWH}{3}$

The base area constitutes of the given equation.

Substitute values into the formula.

$V = \frac{12(4)}{3} = 4(4) = 16$

The answer is:

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Example Question #1614 : Ged Math

Find the volume of a square pyramid if the base area is 2, and the height is 5.

Possible Answers:

$\frac{10}{3}$

$\textup{There is not enough information.}$

Correct answer:

$\frac{10}{3}$

Explanation:

Write the formula for the volume of a pyramid.

$V =\frac{LWH}{3}$

The base area constitutes , and can be replaced with the numerical area.

$V =\frac{LWH}{3} =\frac{BH}{3} = \frac{2\times 5}{3} =\frac{10}{3}$

The answer is: $\frac{10}{3}$

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Example Question #1615 : Ged Math

If the length, width, and height of a pyramid is 2, 7, and 9, respectively, what must be the volume?

Possible Answers:

180

126

Correct answer:

Explanation:

Write the formula for the volume of a pyramid.

$V= \frac{LWH}{3} = \frac{2(7)(9)}{3} = 2(7)(3) = 42$

The answer is:

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #41 : Volume Of A Cylinder

Example Question #1611 : Ged Math

Example Question #92 : 3 Dimensional Geometry

Example Question #1612 : Ged Math

Example Question #93 : 3 Dimensional Geometry

Example Question #1613 : Ged Math

Example Question #2 : Volume Of A Pyramid

Example Question #4 : Volume Of A Pyramid

Example Question #1614 : Ged Math

Example Question #1615 : Ged Math

All GED Math Resources

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