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High School Math : How to find the volume of a pyramid

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Example Question #1 : Pyramids

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

Possible Answers:

285

105

245

175

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 #2 : Pyramids

Find the volume of the following pyramid.

Pyramid

Possible Answers:

$96\sqrt{7}m^3$

$96\sqrt{3}m^3$

$48\sqrt{7}m^3$

$48\sqrt{3}m^3$

$96\sqrt{5}m^3$

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

What is the sum of the number of vertices, edges, and faces of a square pyramid?

Possible Answers:

Correct answer:

Explanation:

A square pyramid has one square base and four triangular sides.

Vertices (where two or more edges come together): 5. There are four vertices on the base (one at each corner of the square) and a fifth at the top of the pyramid.

Edges (where two faces come together): 8. There are four edges on the base (one along each side) and four more along the sides of the triangular faces extending from the corners of the base to the top vertex.

Faces (planar surfaces): 5. The base is one face, and there are four triangular faces that form the top of the pyramid.

Total = 5 + 8 + 5 = 18

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

An architect wants to make a square pyramid and fill it with 12,000 cubic feet of sand. If the base of the pyramid is 30 feet on each side, how tall does he need to make it?

Possible Answers:

$13.3\ ft$

$40\ ft$

$26.7\ ft$

$30\ ft$

$50\ ft$

Correct answer:

$40\ ft$

Explanation:

Volume of Pyramid = 1/3 * Area of Base * Height

12,000 ft³ = 1/3 * 30ft * 30ft * H

12,000 = 300 * H

H = 12,000 / 300 = 40

H = 40 ft

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

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Possible Answers:

$2\ ft^{2}$

$4\ ft^{2}$

$1.5\ ft$

$2\ ft$

$4\ ft$

Correct answer:

$2\ ft$

Explanation:

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

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High School Math : How to find the volume of a pyramid

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Pyramids

Example Question #1 : Pyramids

Example Question #2 : Pyramids

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

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

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

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