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=(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=(1)/(3)\cdot b^2\cdot h \\ \\ V=(1)/(3)\cdot900 \\ V=300\text{ in\textasciicircum{}3} \end{gathered}`

the volume of the pyramid is 300 cubic inches