A closed cylindrical can has a surface area of 120$\pi$ square inches.Express the volume of the can as a function of its radius,r.
A)V(r)= 60$\pi$r cubic inches
B) $V ( r ) = 120 \pi r ^ { 2 }$ cubic inches
C) $V ( r ) = \pi \left( 60 - r ^ { 3 } \right)$ cubic inches
D) $V ( r ) = \pi r \left( 60 - r ^ { 2 } \right)$ cubic inches

Question

Quizplus · Accepted Answer

The surface area of a cylinder is given by $2\pi r^2 + 2\pi rh = 120\pi$, where $r$ is the radius and $h$ is the height. Solving for $h$ gives $h = 60/r - r$. The volume of a cylinder is $V = \pi r^2h$, substituting $h$ gives $V(r) = \pi r^2(60/r - r) = \pi r(60 - r^2)$.

A Closed Cylindrical Can Has a Surface Area of 120 π\piπ

A Closed Cylindrical Can Has a Surface Area of 120 $\pi$