Question

WRITING

How is the formula for the volume of a pyramid different from the formula for the volume of a prism?

Answer 1

Hint: Compare the volume of the pyramid with the volume of the prism.

Assume that the base of the prism and base of the pyramid have the same shape.

Let’s assume the area of the base of the prism is $B_1$ & the area of the base of the pyramid is $B_2$.

The formula of the volume of the prism is given by: $V\left(\mathrm{prism}\right)=Bh$

Where $B$ is the area of the base & $h$ is the height of the prism.

As the pyramid tapers towards the top, The formula of the volume of the pyramid is given by: $V\left(\mathrm{pyramid}\right)=\frac{1}{3}Bh$

Where $B$ is the area of the base & $h$ is the height of the pyramid.

$V=\frac{1}{3}(Volumeoftheprism)$

Final Answer: Hence, The volume of the pyramid is one-third of the volume of the prism.