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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 #1601 : Ged Math

Find the volume of a cylinder with a radius of 3 and a height of 30.

Possible Answers:

$90\pi$

$270\pi$

$180\pi$

$2700\pi$

$540\pi$

Correct answer:

$270\pi$

Explanation:

Write the formula for the volume of a cylinder.

$V = \pi r^2h$

Substitute the dimensions.

$V = \pi (3)^2(30) = \pi (9)(30) = 270\pi$

The answer is: $270\pi$

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Example Question #36 : Volume Of A Cylinder

Find the volume of the cylinder if the radius is $3\pi$ and the height is $5\pi$ .

Possible Answers:

$15\pi^2$

$15\pi^3$

$9\pi ^4$

$90\pi ^4$

$45\pi ^4$

Correct answer:

$45\pi ^4$

Explanation:

Write the formula for a cylinder.

$V= \pi r^2h$

Substitute the dimensions.

$V= \pi (3\pi)^2(5\pi) = 45\pi ^4$

The answer is: $45\pi ^4$

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Example Question #37 : Volume Of A Cylinder

Find the volume of the cylinder with a base area of 9, and a height of $2\pi$ .

Possible Answers:

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

$18\pi$

$81\pi^2$

$162\pi ^2$

$162\pi$

Correct answer:

$18\pi$

Explanation:

Write the formula for the volume of a cylinder.

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

The base is a circular shape, and its area is already provided. This means we can substitute the base area for $\pi r^2$ .

$V= 9(2\pi)$

The answer is: $18\pi$

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Example Question #1602 : Ged Math

You are filling a cylindrical hole with concrete, and need to know how much concrete to mix. If the hole is deep and has a radius of 6 inches, what volume of concrete will be needed to fill the hole?

Possible Answers:

5.25ft^3

3.93ft^3

1.25ft^3

3.14ft^3

Correct answer:

3.93ft^3

Explanation:

You are filling a cylindrical hole with concrete, and need to know how much concrete to mix. If the hole is deep and has a radius of , what volume of concrete will be needed to fill the hole?

Our formula for volume of a cylinder is:

$V=\pi r^2 h$

Now, before we start plugging stuff in, we need to have all our measurements be in the same units. Let's switch to feet so that we are consistent.

$6in=\frac{1}{2}ft$

Now, let's plug it in and solve:

$V=\pi (\frac{1}{2}ft)^2 (5ft)=\pi \frac{5}{4}ft^3=3.93ft^3$

So, we need

3.93ft^3 of concrete

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Example Question #1602 : Ged Math

In order for Helen to clean her cylindrical fish tank, she must first empty out half the water. If the fish tank has a radius of inches and a height of inches, what is the volume of water, in cubic inches, that she will need to empty? Let $\pi=3.14$ .

Possible Answers:

2880

3450

2950

3140

Correct answer:

3140

Explanation:

Recall how to find the volume of a cylinder:

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

Since Helen is only taking out half the water, we will need to find half the volume of the cylindrical fish tank. Thus, we can write the following equation:

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

Plug in the given radius and height to find the volume of water that Helen needs to remove.

$\text{Volume Removed}=\frac{(3.14) 10^2(20)}{2}=3140in^3$

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Example Question #83 : 3 Dimensional Geometry

While exploring the woods near your house, you find a cylindrical hole in the ground. You decide that it is dangerous and should be filled in with concrete so that nobody falls in and hurts themselves. You find that the hole is 20 feet deep and 6 feet wide. How many cubic feet of concrete will you need to fill in the hole?

Possible Answers:

262.5ft^3

180ft^3

565.5ft^3

366ft^3

Correct answer:

565.5ft^3

Explanation:

We need to find the volume of a cylinder. Use the following formula

$V=\pi r ^2 h$

A cylinder is really just a circle with height.

We know our height, 20ft.

Our radius is half of the width of the hole. In this case, our width is 6ft, so our radius is 3 ft.

Plug these in and find our volume.

$V=\pi (3ft) ^2 20ft=\pi 180ft^3=565.5ft^3$

So our answer is:

565.5ft^3

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Example Question #1604 : Ged Math

How much water would be required to fill a tube which is 3 ft wide and 18 ft long?

Possible Answers:

$V= 45.25\pi ft^3$

$V= 20.5\pi ft^3$

$V= 40.5\pi ft^3$

V= 40.5 ft^3

Correct answer:

$V= 40.5\pi ft^3$

Explanation:

How much water would be required to fill a tube which is 3 ft wide and 18 ft long?

We are indirectly asked to find the volume of a cylinder. To do so, we need to following formula:

$V=\pi r^2h$

Where r is the radius of our cylinder, and h is the height.

First, we need to change our diameter (3ft) to our radius. The radius is always half the diameter, so our radius is 1.5 ft

Next, plug in our radius and height and solve for V.

$V=\pi (1.5ft)^2(18ft)= 40.5\pi ft^3$

So, we have our answer:

$V= 40.5\pi ft^3$

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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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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1601 : Ged Math

Example Question #36 : Volume Of A Cylinder

Example Question #37 : Volume Of A Cylinder

Example Question #1602 : Ged Math

Example Question #1602 : Ged Math

Example Question #83 : 3 Dimensional Geometry

Example Question #1604 : Ged Math

Example Question #91 : 3 Dimensional Geometry

Example Question #1603 : Ged Math

Example Question #1604 : Ged Math

All GED Math Resources

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