Solve the Problem $S ( r ) = 4 \pi r ^ { 2 }$

question 466

Multiple Choice

Solve the problem.
-The surface area of a balloon is given by $S ( r ) = 4 \pi r ^ { 2 }$ , where $r$ is the radius of the balloon. If the radius is increasing with time $t$ , as the balloon is being blown up, according to the formula $r ( t ) = \frac { 2 } { 3 } t ^ { 3 }$ , $t \geq 0$ , find the surface area $S$ as a function of the time $t$ .

• A) \(S ( r ( t ) ) = \frac { 16 } { 9 } \pi t ^ { 6 }\)
• B) \(S ( r ( t ) ) = \frac { 16 } { 9 } \pi t ^ { 9 }\)
• C) \(S ( r ( t ) ) = \frac { 4 } { 9 } \pi t ^ { 6 }\)
• D) \(S ( r ( t ) ) = \frac { 16 } { 9 } \pi t ^ { 3 }\)

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