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GED Math : 3-Dimensional Geometry

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Example Questions

Example Question #91 : 3 Dimensional Geometry

A cylindrical soft drink can has a radius of cm and a height of cm. In cubic centimeters, what volume of soft drink does the can hold? Round your answer to the nearest hundredths place.

Possible Answers:

133.58

193.40

142.59

175.93

Correct answer:

175.93

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume}=\pi r^2 h$

Plug in the given radius and height to find the volume.

$\text{Volume}=\pi (2)^2(14)=56\pi=175.93$

The soft drink can is able to hold a volume of 173.93 cubic centimeters of liquid.

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Example Question #1603 : Ged Math

If a cylinder has a height of inches and a diameter of inches, what is its volume?

Possible Answers:

$53.2\pi$ squared inches

$48\pi$ cubed inches

$12\pi$ cubed inches

$53.2\pi$ cubed inches

81.3 squared inches

Correct answer:

$48\pi$ cubed inches

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 diameter. 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 diameter? 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 inches.

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

$V = \pi \times 4^{2} \times 3$

$V = \pi \times 16 \times 3$

$V= \pi \times 48$

$V = 48\pi$ cubed inches

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Example Question #1604 : Ged Math

If a right cylinder has a diameter of and a height that is three times the radius, what is its volume?

Possible Answers:

$36\pi$

$648\pi$

$18\pi$

Correct answer:

$648\pi$

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 kind of) and the diameter. This problem provides a slight curve ball in that we indirectly have been given the radius and height, so we need to do some detective work. What is the relationship between radius and diameter? 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 . Now we can figure out the value of the height. The problem says it is three times the radius. Therefore, $6 \times 3 = 18$ , so the height is 18.

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

$V = \pi \times 6^{2} \times 18$

$V = \pi \times 36 \times 18$

$V= \pi \times 648$

$V = 648\pi$ cubed units

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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!

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 #91 : 3 Dimensional Geometry

Pyramid_1

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

Possible Answers:

14.1

17.3

6.7

5.8

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 #93 : 3 Dimensional Geometry

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 #94 : 3 Dimensional Geometry

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

Possible Answers:

160

720

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

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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GED Math : 3-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #91 : 3 Dimensional Geometry

Example Question #1603 : Ged Math

Example Question #1604 : Ged Math

Example Question #41 : Volume Of A Cylinder

Example Question #91 : 3 Dimensional Geometry

Example Question #92 : 3 Dimensional Geometry

Example Question #93 : 3 Dimensional Geometry

Example Question #93 : 3 Dimensional Geometry

Example Question #94 : 3 Dimensional Geometry

Example Question #2 : Volume Of A Pyramid

All GED Math Resources

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