Application of Derivatives 2 Question 1
1. A spherical iron ball of radius is coated with a layer of ice of uniform thickness that melts at a rate of . When the thickness of the ice is , then the rate at which the thickness (in ) of the ice decreases, is
(2019 Main, 10 April II)
(a)
(b)
(c)
(d)
Show Answer
Solution:
- Let the thickness of layer of ice is
, the volume of spherical ball (only ice layer) is
On differentiating Eq. (i) w.r.t. ’
[-ve sign indicate that volume is decreasing as time passes].
At
So, the thickness of the ice decreases at the rate of