Question

Write an expression in factored form to represent the volume in the canister not occupied by the tennis balls.

Assume the canister is cylinder with volume V = π r2 h.

Answer 1

Canister is a cylinder

`\\ \rm\rightarrowtail V=\pi r^2h-3((4)/(3)\pi r^3)`

`\\ \rm\rightarrowtail V=\pi r^2h-(12)/(3)\pi r^3`

`\\ \rm\rightarrowtail V=\pi r^2h-4\pi r^3`

• Take πr^2 common

`\\ \rm\rightarrowtail V=\pi r^2(h-4r)`

Answer 2

`\implies V=\pi r^2(h-4 r)`

Explanation:

Volume of the canister LESS the volume of 3 tennis balls:

`V=\pi r^2h-3\left(\frac43\pi r^3\right)`

Expand brackets:

`\implies V=\pi r^2h-4\pi r^3`

Factor:

`\implies V=\pi r^2(h-4 r)`