Application of DerivativeHard

Question

The surface area of a spherical bubble is increasing at the rate of 2 cm2/s. When the radius of the bubble is 6 cm, then the rate by which the volume of the bubble increasing is-

Options

A.6 cm3/sec
B.9 cm3/sec
C.3 cm3/sec
D.12 cm3/sec

Solution

A = 4πr2
⇒  = 8 π r
⇒  2 = 8 . π . 6 .
[∵ = 2cm2/sec    &    r = 6 cm]
⇒ cm/sec
Now V = π r3
⇒ ⇒  4 . π r2
⇒  
⇒  = 6 cm3/sec.

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