An Offshore Oil Well Is Leaking Oil and Creating a Circular

Multiple Choice

An offshore oil well is leaking oil and creating a circular oil slick. If the radius of the slick is growing at a rate of 7 miles per hour, find the rate at which the area is increasing when the radius is 3 miles. (The area of a disc of radius r is $A = \pi r ^ { 2 }$ .)

A) $\frac { \mathrm { d } A } { \mathrm {~d} t } = 9 \pi \frac { \mathrm { mi } ^ { 2 } } { \mathrm { hr } }$
B) $\frac { \mathrm { d } A } { \mathrm {~d} t } = 14 \pi \frac { \mathrm { mi } ^ { 2 } } { \mathrm { hr } }$
C) $\frac { \mathrm { d } A } { \mathrm {~d} t } = 42 \pi \frac { \mathrm { mi } ^ { 2 } } { \mathrm { hr } }$
D) $\frac { \mathrm { d } A } { \mathrm {~d} t } = 7 \pi \frac { \mathrm { mi } ^ { 2 } } { \mathrm { hr } }$
E) $\frac { \mathrm { d } A } { \mathrm {~d} t } = 21 \pi \frac { \mathrm { mi } ^ { 2 } } { \mathrm { hr } }$