Questions
The radius of an air bubble is increasing at the rate of cms-1. Determine the rate of increase in it's volume when the radius is 1 cm.
a
6.29 cm2s2
b
6.28 cm4s-3
c
6.28 cm3s-1
d
6.28 cm3s-4
detailed solution
Correct option is C
Volume of the spherical bubble v=43πR3differentiating both sides w.r.t. time dVdt=ddt43πR3⇒dVdt=43π3R2dRdt ⇒dVdt=4πR2dRdtat R=1 cm and when dRdt=12 cms-1, we have dVdt=4π×12×12 =2π cm3s-1 =6.28 cm3s-1Talk to our academic expert!
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