Question

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

Answer 1

Canister is a cylinder

$\\ \rm\rightarrowtail V=\pi r^2h-3(\dfrac{4}{3}\pi r^3)$

$\\ \rm\rightarrowtail V=\pi r^2h-\dfrac{12}{3}\pi r^3$

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

• Take πr^2 common

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

Answer 2

Answer:

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

Step-by-step explanation:

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

$V=\pi r^2h-3\left(\dfrac43\pi r^3\right)$

Expand brackets:

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

Factor:

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