Question

A square pyramid and a square prism have the same length, width, and height. If the volume of the square prism is 900in3 , what is the volume of the square pyramid?

Answer 1

A square pyramid and a square prism have the same length, width, and height. If the volume of the square prism is 900in3 , what is the volume of the square pyramid?

we know that

The volume of the square prism is equal to

$V=b^2\cdot h$

where b is the length side of the square base and h is the height of the prism

The volume of the square pyramid is

$V=\frac{1}{3}\cdot b^2\cdot h$

Remember that

the volume of the square prism is 900in3

so

$900=b^2\cdot h$

substitute in the formula of volume of the pyramid

$\begin{gathered} V=\frac{1}{3}\cdot b^2\cdot h \\ \\ V=\frac{1}{3}\cdot900 \\ V=300\text{ in\textasciicircum{}3} \end{gathered}$

the volume of the pyramid is 300 cubic inches