Question

If the volume of a cone is 325 cubic units, what will be the volume of a cylinder withsame height and base as the cone?

Answer 1

The volume of a cone is given by:

$V^{\prime}=\frac{1}{3}\pi r^2h$

where, r is the radius and h is the height. The volume of a cylinder is:

$V=\pi r^2h$

where r is the radius and h is the height.

From these expressions we notice that the volume of a cone is a third of the volume of a cylinder with the same height a base, then we have:

$V^{\prime}=\frac{1}{3}V$

If the volume of the cone is 325 then we have:

$\begin{gathered} 325=\frac{1}{3}V \\ V=(3)(325) \\ V=975 \end{gathered}$

Therefore, the volume of the cylinder is 975 cubic units.