If the volume of a spherical ball is increasing at the rate of 4 π   cc / sec then the rate of…

If the volume of a spherical ball is increasing at the rate of 4π cc/sec then the rate of increase of its radius in cm/sec, when the volume is 288π cc is 
  1. 1 9
  2. 1 6
  3. 1 2 4
  4. 1 3 6

Solution

Volume of sphere of radius r is V=43πr3

Given V=288π cc

⇒288π=43πr3

⇒r3=288×34=216

⇒r=6 cm.

Again, V=43πr3

Differentiate w.r.t. 't'

⇒dVdt=4πr2drdt

Put the given values, to get

⇒4π=4π×62×drdt

⇒drdt=136 cm/sec.

Asked in: JEE Main 2014 (19 Apr Online)

Practice more Applications of Derivatives questions on Aicharya