Question

A cone with a height of 9 inches and a radius of 4 inches is placed on top of a cylinder with a radius of 4 inches and unknown height. Using 3.14 for π, the volume of the combined figure is 653.12 cubic inches. Given this information, what is the height of the cylinder?

Answer 1

check the picture below.

thus, the radius of each is 4 inches, and the heights are 9 and "h" respectively.

the volume of the figure is the volume of the cone plus the volume of the cylinder then, thus


`\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\qquad \qquad \implies V=\cfrac{\pi 4^2\cdot 9}{3}\implies V=48\pi \\\\\\ \textit{volume of a cylinder}\\\\ V=\pi r^2 h\qquad \qquad \implies V=\pi 4^2\cdot h\implies V=16\pi h\\\\ -------------------------------\\\\ \stackrel{\textit{cone's volume}}{48\pi }+\stackrel{\textit{cylinder's volume}}{16\pi h}=653.12\implies 16\pi h=653.12-48\pi \\\\\\ h=\cfrac{653.12-48\pi }{16\pi }`