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A spherical balloon is being inflated at...

A spherical balloon is being inflated at the rate of 35 cc/min. The rate of increase of the surface area of the bolloon when its diameter is 14 cm is

A

7 sq. cm/min

B

10 sq.cm/min

C

17.5 sq. cm/min

D

28 sq. cm/min

Text Solution

Verified by Experts

The correct Answer is:
B
Volume`=V=(4)/(3)pir^(3)implies(dV)/(dt)=4pir^(2).(dr)/(dt)`, at `r=7cm`
`35(cc)/(min)=4pi(7)^(2)(dr)/(dt)implies(dr)/(dt)=(5)/(28pi)`
Surface area, `S=4pir^(2)`
`(dS)/(dt)=8pir(dr)/(dt)=(8pi.7.5)/(28pi)=10(cm^(2))/(min)`
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