Question

A tennis ball has a radius of 3.4 cm. What volume of this cylinder is empty?

Answer 1

Thanks to point

ok nerd

Answer 2

check the picture below.

so, now, we simply get the volume of the cylinder, and then volume of the 3 balls, and subtract the volume of the balls from the cylinders, effectively making a hole in the volume of the cylinder, and what's leftover, is the empty area.


`\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~ \begin{cases} r=3.4\\ h=20.4 \end{cases}\implies V=\pi \cdot 3.4^2\cdot 20.4\implies V=235.824\pi \\\\ -------------------------------\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad r=3.4\implies V=\cfrac{4\cdot \pi \cdot 3.4^3}{3}\implies V=\cfrac{157.216\pi }{3}`


`\bf \textit{volume of the \underline{3 balls}}\quad 3\cdot \cfrac{157.216\pi }{3}\implies 157.216\pi \\\\ -------------------------------\\\\ \stackrel{\textit{volume of the cylinder}}{235.824\pi }-\stackrel{\textit{volume of the balls}}{157.216\pi }\implies 78.608\pi`