A Rather Flimsy Spherical Balloon Is Designed to Pop at the Instant

Multiple Choice

A rather flimsy spherical balloon is designed to pop at the instant its radius has reached 5 cm. Assuming the balloon is filled with helium at a rate of $10 \frac { \mathrm { cm } ^ { 3 } } { \mathrm {~s} }$ , calculate how fast the diameter is growing at the instant it pops. Round your answer to the three decimal places.
The volume of a sphere of radius r is $V = \frac { 4 } { 3 } \pi r ^ { 3 }$ .

A) $0.255 \frac { \mathrm { cm } } { \mathrm { s } }$
B) $0.064 \frac { \mathrm { cm } } { \mathrm { s } }$
C) $0.318 \frac { \mathrm { cm } } { \mathrm { s } }$
D) $0.032 \frac { \mathrm { cm } } { \mathrm { s } }$
E) $0.424 \frac { \mathrm { cm } } { \mathrm { s } }$