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Pre-Algebra : Volume of a Pyramid

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Example Questions

Example Question #11 : Volume Of A Pyramid

Find the volume of a pyramid with a length of 2, width of 6, and a height of 9.

Possible Answers:

108 $\displaystyle 108$

$\displaystyle 36$

$\displaystyle 72$

$\displaystyle 17$

$\displaystyle 84$

Correct answer:

$\displaystyle 36$

Explanation:

Write the formula for the volume of a pyramid.

$V=\frac{1}{3} (\textup{ Length} \times\textup{ Width} \times\textup{ Height})$ $\displaystyle V=\frac{1}{3} (\textup{ Length} \times\textup{ Width} \times\textup{ Height})$

Substitute the given length, width, and height.

$V=\frac{1}{3} (2\times6\times9)$ $\displaystyle V=\frac{1}{3} (2\times6\times9)$

Rewrite the $\displaystyle 6$ inside the parentheses as a factor of $\displaystyle 3$ .

$V=\frac{1}{3} (2\times (3 \times 2)\times9)$ $\displaystyle V=\frac{1}{3} (2\times (3 \times 2)\times9)$

Cancel the fraction with the three and multiply the terms to get the volume.

$V=2\times 2\times 9 = 36$ $\displaystyle V=2\times 2\times 9 = 36$

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Example Question #201 : Geometry

Find the volume of a pyramid if the dimensions of the length, width, and height are 3,5,10 $\displaystyle 3,5,10$ , respectively.

Possible Answers:

150 $\displaystyle 150$

120 $\displaystyle 120$

100 $\displaystyle 100$

$\displaystyle 50$

450 $\displaystyle 450$

Correct answer:

$\displaystyle 50$

Explanation:

Write the volume formula for a pyramid.

$V=\frac{1}{3}( \textup{Length} \times \textup{Width } \times \textup{Height})$ $\displaystyle V=\frac{1}{3}( \textup{Length} \times \textup{Width } \times \textup{Height})$

Plug in the dimensions.

$V=\frac{1}{3}( 3\times5 \times 10)=\frac{3\times5 \times 10}{3}$ $\displaystyle V=\frac{1}{3}( 3\times5 \times 10)=\frac{3\times5 \times 10}{3}$

Cancel out the three on the numerator and denominator.

$V=5\times 10$ $\displaystyle V=5\times 10$

Multiply.

V=50 $\displaystyle V=50$

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Example Question #13 : Volume Of A Pyramid

Find the volume of a pyramid with a length of 6cm, a width that is half the length, and a height that is two times the length.

Possible Answers:

$36\text{cm}^3$ $\displaystyle 36\text{cm}^3$

$216\text{cm}^2$ $\displaystyle 216\text{cm}^2$

$72\text{cm}^3$ $\displaystyle 72\text{cm}^3$

$108\text{cm}^3$ $\displaystyle 108\text{cm}^3$

$108\text{cm}^2$ $\displaystyle 108\text{cm}^2$

Correct answer:

$72\text{cm}^3$ $\displaystyle 72\text{cm}^3$

Explanation:

The formula for volume of a pyramid is

$V =\frac{ l \cdot w \cdot h}{3}$ $\displaystyle V =\frac{ l \cdot w \cdot h}{3}$

where l is the length, w is the width, and h is the height. We know the length is 6cm. The width is half the length, so the width is 3cm. The height is two times the length, so the height is 12cm. Using this information, we substitute. We get

$V =\frac{ 6\text{cm} \cdot 3\text{cm} \cdot 12\text{cm}}{3}$ $\displaystyle V =\frac{ 6\text{cm} \cdot 3\text{cm} \cdot 12\text{cm}}{3}$

$V =\frac{ 216}{3}\text{cm}^3=72 \text{cm}^3$ $\displaystyle V =\frac{ 216}{3}\text{cm}^3=72 \text{cm}^3$

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Pre-Algebra : Volume of a Pyramid

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #11 : Volume Of A Pyramid

Example Question #201 : Geometry

Example Question #13 : Volume Of A Pyramid

All Pre-Algebra Resources

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