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:

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)  80 text π text cu text m/s  (B)  text144 π text cu text m/s  (C) 80 cu m/s (D) 64 cu m/s

Tardigrade Admin · Accepted Answer

Let h and r be the height and radius of cylinder. Given that

\frac{d r}{d t} = 3 m / s, \frac{d h}{d t} = - 4 m / s .

Also, On differentiating w.r.t. t

\frac{d V}{d t} = π [r^{2} \frac{d h}{d t} + h .2 r \frac{d r}{d t}]

At

r = 4 m an d h = 6 m

\frac{d V}{d t} = π [- 64 + 144]

= 80 π c u m / s

Q. 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:

$80 π c u m / s$

$144 π c u m / s$

80 cu m/s

64 cu m/s

$- 80 π c u m / s$

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

80πcum/s

144 πcum/s