Solve the problem.
-An oil well off the Gulf Coast is leaking, with the leak spreading oil over the surface of the gulf as a circle. At any time t, in minutes, after the beginning of the leak, the radius of the oil slick on the surface is r(t) = 3t ft. Find
The area A of the oil slick as a function of time.
A) $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t } ^ { 2 }$
B) $A ( r ( t ) ) = 9 t ^ { 2 }$
C) $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t }$
D) $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 3 \pi \mathrm { t } ^ { 2 }$

Question

Solve the problem.
-An oil well off the Gulf Coast is leaking, with the leak spreading oil over the surface of the gulf as a circle. At any time t, in minutes, after the beginning of the leak, the radius of the oil slick on the surface is r(t) = 3t ft. Find
The area A of the oil slick as a function of time. 
A) $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t } ^ { 2 }$
B) $A ( r ( t ) ) = 9 t ^ { 2 }$
C) $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t }$
D) $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 3 \pi \mathrm { t } ^ { 2 }$

Quizplus · Accepted Answer

The area of a circle is given by $A = \pi r^2$. Since $r(t) = 3t$, substituting $r(t)$ into the area formula gives $A = \pi (3t)^2 = 9\pi t^2$.

Solve the Problem A(r(t))=9πt2\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t } ^ { 2 }A(r(t))=9πt2

Solve the Problem $\mathrm { A } ( \mathrm { r } ( \mathrm { t } ) ) = 9 \pi \mathrm { t } ^ { 2 }$