Question

What is the new volume of a right square pyramid with a volume 180in.3 if the lengths of the sides of the base remain fixed but it’s height is multiplied by a factor 10

Answer 1

The volume of a right square pyramid is $V= \frac{1}{3} A_{\text{ basis } }\cdot h$, where $A_{\text{ basis } }$ is basis area.

If the lengths of the sides of the base remain fixed and height
is multiplied by a factor 10, than new height is $H=10h$ and the volume is

$V^{\ast}=A_{\text{ basis } }\cdot H=\frac{1}{3} A_{\text{ basis } }\cdot 10h=\frac{10}{3} A_{\text{ basis } }\cdot h$