The Soap Bubble I Am Blowing Has a Radius That $S = 4 \pi r ^ { 2 }$

question 71

Multiple Choice

The soap bubble I am blowing has a radius that is growing at a rate of 3 cm/s. How fast is the surface area growing when the radius is 10 cm (The surface area of a sphere of radius r is $S = 4 \pi r ^ { 2 }$ .)

• A) \(\frac { \mathrm { d } S } { \mathrm {~d} t } = 85 \pi \frac { \mathrm { cm } ^ { 2 } } { \mathrm {~s} }\)
• B) \(\frac { \mathrm { d } S } { \mathrm {~d} t } = \frac { 240 } { \pi } \frac { \mathrm { cm } ^ { 2 } } { \mathrm {~s} }\)
• C) \(\frac { \mathrm { d } S } { \mathrm {~d} t } = 240 \pi \frac { \mathrm { cm } ^ { 2 } } { \mathrm {~s} }\)
• D) \(\frac { \mathrm { d } S } { \mathrm {~d} t } = 243 \pi \frac { \mathrm { cm } ^ { 2 } } { \mathrm {~s} }\)
• E) \(\frac { \mathrm { d } S } { \mathrm {~d} t } = 24 \pi \frac { \mathrm { cm } ^ { 2 } } { \mathrm {~s} }\)

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