Question

The volume of a cylinder is 24(pi) ft3. What is the volume of a cone that has the same base and height?

Answer 1

`\bf \begin{array}{llll} \textit{volume of a cylinder}\\\\ V=\pi r^2 h \end{array}\qquad \qquad \qquad \begin{array}{llll} \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\implies \cfrac{1}{3}(\pi r^2 h) \end{array}`

now, if you notice there, for a cylinder with radius "r" and height "h", that is its volume.

and for a cone that has the same "h" and "r' as the cylinder's, that is its volume, however, notice, the cone's volume is one third of that of the cylinder's.

so if the cylinder has a volume of 24, well, you already know what is the cone's.