A spherical tank for liquefied petroleum is 16 in. in diameter. What is the ratio of surface area to the volume of the tank?
A) $\frac { \pi } { 8 }$
B) $\frac { 8 } { 3 }$
C) $\frac { 2 } { 1 }$
D) $\frac { 3 } { 8 \pi }$
E) $\frac { 3 } { 8 }$

Question

Quizplus · Accepted Answer

The surface area of a sphere is given by $4\pi r^2$ and the volume is given by $\frac{4}{3}\pi r^3$. Therefore, the ratio of surface area to volume is $\frac{4\pi r^2}{\frac{4}{3}\pi r^3}=\frac{3}{r}$. Substituting $r=8$ inches, we get $\frac{3}{8}$.

A Spherical Tank for Liquefied Petroleum Is 16 In π8\frac { \pi } { 8 }8π​

A Spherical Tank for Liquefied Petroleum Is 16 In $\frac { \pi } { 8 }$