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High School Math : Geometry

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Example Questions

Example Question #2 : How To Find The Volume Of A Cube

What is the difference in volume between a sphere with radius x and a cube with a side of 2x? Let π = 3.14

Possible Answers:

4.18x³

8.00x³

3.82x³

5.28x³

6.73x³

Correct answer:

3.82x³

Explanation:

V_cube = s³ = (2x)³ = 8x³

V_sphere = 4/3 πr³ = 4/3•3.14•x³ = 4.18x³

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Example Question #3 : How To Find The Volume Of A Figure

The density of gold is $16\ g/cm^3$ and the density of glass is $2\ g/cm^3$ . You have a gold cube that is $x\ cm$ in length on each side. If you want to make a glass cube that is the same weight as the gold cube, how long must each side of the glass cube be?

Possible Answers:

2.5x

1.5x

Correct answer:

Explanation:

Weight = Density * Volume

Volume of Gold Cube = side³= x³

Weight of Gold = 16 g/cm³* x³

Weight of Glass = 3/cm³ * side³

Set the weight of the gold equal to the weight of the glass and solve for the side length:

16* x³ = 2 * side³

side³ = 16/2* x³= 8 x³

Take the cube root of both sides:

side = 2x

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Example Question #1 : How To Find The Volume Of A Cube

A cube has edges that are three times as long as those of a smaller cube. The volume of the bigger cube is how many times larger than that of the smaller cube?

Possible Answers:

Correct answer:

Explanation:

If we let represent the length of an edge on the smaller cube, its volume is $x^{3}$ .

The larger cube has edges three times as long, so the length can be represented as . The volume is $(3x)^{3}$ , which is $27x^{3}$ .

The large cube's volume of $27x^{3}$ is 27 times as large as the small cube's volume of $x^{3}$ .

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Example Question #1 : How To Find The Volume Of A Cube

If a cube has its edges increased by a factor of 5, what is the ratio of the new volume to the old volume?

Possible Answers:

25:1

100:1

15:1

5:1

125:1

Correct answer:

125:1

Explanation:

A cubic volume is side*side*side . Let the original sides be 1, so that the original volume is 1. Then find the volume if the sides measure 5. This new volume is 125. Therefore, the ratio of new volume to old volume is 125: 1.

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Example Question #11 : How To Find The Volume Of A Cube

A cube has a side length of meters. What is the volume of the cube?

Possible Answers:

$6\ \textup{m}^{3}$

$16\ \textup{m}^{3}$

$2\ \textup{m}^{3}$

$4\ \textup{m}^{3}$

$8\ \textup{m}^{3}$

Correct answer:

$8\ \textup{m}^{3}$

Explanation:

The formula for the volume of a cube is:

$Volume = (side)^{3}$

Since the length of one side is meters, the volume of the cube is:

$2^{3 } = 8$ meters cubed.

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Example Question #12 : How To Find The Volume Of A Cube

If the length of the side of a cube is $8x^{2}$ , which expression represents the volume of the cube?

Possible Answers:

$64x^{6}$

$512x^{6}$

$8x^{3}$

none of the other answers

$512x^{3}$

Correct answer:

$512x^{6}$

Explanation:

The formula for the volume of the cube is $V = x^{3}$

Plugging that into Volume equation, we find $8^{3}$ and $(x^{^{2)^{3}}}$

Thus, the answer is 512x⁶

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Example Question #4 : How To Find The Volume Of A Cube

A tank measuring 3in wide by 5in deep is 10in tall. If there are two cubes with 2in sides in the tank, how much water is needed to fill it?

Possible Answers:

150 in^3

134 in^3

8 in^3

16 in^3

160 in^3

Correct answer:

134 in^3

Explanation:

$Volume_{Tank} = Width \cdot Depth \cdot Height$

$Volume_{Tank} = 3in \cdot 5in \cdot 10in = 150 in^3$

$Volume_{Cube} = (Side)^3 = (2in)^3 = 8 in^3$

$Volume_{Water}=Volume_{Tank}-2(Volume_{Cube})$

$Volume_{Water}=150-2(8)$

$Voume_{Water}=150-16$

$Volume_{Water}=134in^3$

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Example Question #1 : How To Find The Volume Of A Pyramid

What is the volume of a pyramid with a height of and a square base with a side length of ?

Possible Answers:

245

105

175

285

Correct answer:

245

Explanation:

To find the volume of a pyramid we must use the equation

$Volume\: of\: pyramid=\frac{1}{3}(area\ of\ base)(height)$

We must first solve for the area of the square using

$A=(side\ length^{2})$

We plug in and square it to get A=49

We then plug our answer into the equation for the pyramid with the height to get

$V=\frac{1}{3}(49)(15)$

We multiply the result to get our final answer for the volume of the pyramid

V=245 .

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Example Question #1 : Pyramids

Find the volume of the following pyramid. Round the answer to the nearest integer.

Pyramid

Possible Answers:

384m^3

364m^3

344m^3

374m^3

354m^3

Correct answer:

364m^3

Explanation:

The formula for the volume of a pyramid is:

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

where is the width of the base, is the length of the base, and is the height of the pyramid.

In order to determine the height of the pyramid, you will need to use the Pythagoream Theorem to find the slant height:

A^2 + B^2 = C^2

A^2 + (5m)^2 = (13m)^2

A^2 = 144m^2

A = 12m

Now we can use the slant height to find the pyramid height, once again using the Pythagoream Theorem:

A^2 + B^2 = C^2

A^2 + (5m)^2 = (12m)^2

A^2 = 119m^2

$A = \sqrt{119}m$

Plugging in our values, we get:

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

$V = \frac{(10m)(10m)(\sqrt{119}m)}{3}$

$V = \frac{100\sqrt{119}m^3}{3} \approx 364m^3$

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Example Question #1 : Pyramids

Find the volume of the following pyramid.

Pyramid

Possible Answers:

$96\sqrt{7}m^3$

$48\sqrt{3}m^3$

$48\sqrt{7}m^3$

$96\sqrt{5}m^3$

$96\sqrt{3}m^3$

Correct answer:

$96\sqrt{7}m^3$

Explanation:

The formula for the volume of a pyramid is:

$V = \frac{1}{3} (base)(height)$

$V = \frac{1}{3} (l)(w)(h)$

Where is the length of the base, is the width of the base, and is the height of the pyramid

Use the Pythagorean Theorem to find the length of the slant height:

A^2 + B^2 = C^2

A^2 + (6m)^2 = (10m)^2

A = 8m

Now, use the Pythagorean Theorem again to find the length of the height:

A^2 + B^2 = C^2

A^2 + (6m)^2 = (8m)^2

$A = 2\sqrt{7}m$

Plugging in our values, we get:

$V = \frac{1}{3} (12m)(12m)(2\sqrt{7}m)$

$V = 96\sqrt{7}m^3$

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High School Math : Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #2 : How To Find The Volume Of A Cube

Example Question #3 : How To Find The Volume Of A Figure

Example Question #1 : How To Find The Volume Of A Cube

Example Question #1 : How To Find The Volume Of A Cube

Example Question #11 : How To Find The Volume Of A Cube

Example Question #12 : How To Find The Volume Of A Cube

Example Question #4 : How To Find The Volume Of A Cube

Example Question #1 : How To Find The Volume Of A Pyramid

Example Question #1 : Pyramids

Example Question #1 : Pyramids

All High School Math Resources

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