How to find the volume of a pyramid

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PSAT Math › How to find the volume of a pyramid

Questions 1 - 3

What is the approximate volume of a square pyramid with one edge of the base measuring $2.7\textup{inches}$ and a height equal to the diagonal of its base?

$9.28\textup{ cubic inches}$

$27.84\textup{ cubic inches}$

$3.82\textup{ cubic inches}$

$14.58\textup{ cubic inches}$

$5.4\textup{ cubic inches}$

Explanation

If one edge of the base is 2.7 inches, and the height of the pyramid is equal to the diagonal of the base, we can find the height using the edge. The height is going to be equal to $\sqrt{2.7^2+2.7^2}=\sqrt{14.58}$ . The area of the base is . Volume of a pyramid is equal to $\left ( \frac{1}{3} \right )\left ( \textup{area of the base} \right )\left ( \textup{height} \right )$

This leaves us with

$v=(7.29)(\sqrt{14.58})\left ( \frac{1}{3} \right )\approx9.28$

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.