If the surface area of a cube is increasing at a rate of 3 . 6 c m 2 / s e c , retaining its shape; then the…

If the surface area of a cube is increasing at a rate of 3.6cm2/sec, retaining its shape; then the rate of change of its volume (in cm3/sec), when the length of a side of the cube is 10cm, is:
  1. 20
  2. 10
  3. 18
  4. 9

Solution

Surface area of cube s=6a2

⇒dsdt=12adadt=3.6

⇒1210dadt=3.6⇒dadt=0.03cm/sec

Now, volume of cube V=a3

⇒dvdt=3a2.dadt=3(10)20.03=9cm3/sec

Asked in: JEE Main 2020 (03 Sep Shift 2)

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