The radius of a cylinder is increasing at the rate of 3 m/s... | Mathematics | SolveeIt | Solveeit

Today, August 19

Question

The radius of a cylinder is increasing at the rate of 3 m/s and its altitude is decreasing at the rate of 4 m/s. The rate of change of volume, when radius is 4 m and altitude is 6 m, is

A

(A) 80πcum/s

B

(B) 144πcum/s

C

(C) 80cum/s

D

(D) 64cum/s

Answer

(A) 80πcum/s

Explanation

Solution

Explanation:
Let h and r be the height and radius of cylinder. Given that drdt=3m/s,dhdt=−4m/sAlso, V=πr2hOn differentiating w.r.t. dVdt=π[r2dhdt+h⋅2rdrdt]At r=4m and h=6mdVdt=π[−64+144]cum/sdVdt=80πcum/s