Answer:
Volume of the cone is increasing at the rate .
Step-by-step explanation:
Given: The radius of a right circular cone is increasing at a rate of in/s while its height is decreasing at a rate of
in/s.
To find: The rate at which volume of the cone changing when the radius is in. and the height is
in.
Solution:
We have,
,
,
,
Now, let be the volume of the cone.
So,
Differentiate with respect to .
Now, on substituting the values, we get
Hence, the volume of the cone is increasing at the rate .