Mark the correct alternative in the following:
A cone whose height is always equal to its diameter is increasing in volume at the rate of 40 cm3/sec. At what rate is the radius increasing when its circular base area is 1 m2?
The volume of a cone, with height h and radius r, is defined by
- (1)
Given that h=2r, we get - (1)
and πr2=1m2=10000cm2, we have to find out
Differentiating (1) with respect to t, we get
Substituting the values, we get
⇒