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GED Math : 3-Dimensional Geometry

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Example Questions

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Example Question #31 : Volume Of A Cylinder

What is the radius of a cylinder if it has a height of and a volume of 1050.25 ?

Possible Answers:

6.33

2.18

4.57

5.09

Correct answer:

4.57

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume}=\pi r^2 h$ , where is the radius, and is the height.

Plug in the given information and solve for the radius.

$1050.25=\pi r^2(16)$

r^2=20.894

r=4.57

The radius of the cylinder is 4.57 .

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Example Question #634 : Geometry And Graphs

Determine the volume of a cylinder with a base area of 10, and a height of 20.

Possible Answers:

200

$200\pi$

$2000\pi$

2000

Correct answer:

200

Explanation:

Write the formula for the volume of the cylinder.

$V = \pi r^2 h$

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

Substitute the base and height into the equation.

V= (10)(20) = 200

The answer is: 200

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Example Question #81 : 3 Dimensional Geometry

Find the volume of the cylinder with a radius of 7 and a height of 10.

Possible Answers:

$\frac{70}{3}\pi$

$490\pi$

$4900\pi$

$\frac{490}{3}\pi$

$70\pi$

Correct answer:

$490\pi$

Explanation:

Write the formula for the volume of a cylinder.

$V= \pi r^2h$

Substitute the radius and height into the equation.

$V= \pi (7)^2(10) = \pi (49) (10) = 490\pi$

The answer is: $490\pi$

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Example Question #82 : 3 Dimensional Geometry

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

Possible Answers:

$180\pi$

$90\pi$

$540\pi$

$2700\pi$

$270\pi$

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 #637 : Geometry And Graphs

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

Possible Answers:

$45\pi ^4$

$90\pi ^4$

$15\pi^2$

$9\pi ^4$

$15\pi^3$

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 #638 : Geometry And Graphs

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

Possible Answers:

$18\pi$

$162\pi ^2$

$81\pi^2$

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

$162\pi$

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 #41 : Volume Of A Cylinder

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:

3.93ft^3

5.25ft^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 #81 : 3 Dimensional Geometry

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:

3450

3140

2880

2950

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 #81 : 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

565.5ft^3

180ft^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 #41 : Volume Of A Cylinder

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

Possible Answers:

$V= 40.5\pi ft^3$

$V= 20.5\pi ft^3$

$V= 45.25\pi ft^3$

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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GED Math : 3-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #31 : Volume Of A Cylinder

Example Question #634 : Geometry And Graphs

Example Question #81 : 3 Dimensional Geometry

Example Question #82 : 3 Dimensional Geometry

Example Question #637 : Geometry And Graphs

Example Question #638 : Geometry And Graphs

Example Question #41 : Volume Of A Cylinder

Example Question #81 : 3 Dimensional Geometry

Example Question #81 : 3 Dimensional Geometry

Example Question #41 : Volume Of A Cylinder

All GED Math Resources

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