Question

# The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder, in cm3/min, when the radius is 2 cm and the height is 3 cm is (The negative sign(-) indicates that volume decreases)

A
2π5
B
8π5
C
3π5
D
2π5

Solution

## The correct option is C 2π5Let r and h be the radius and height of the cylinder respectively. Given, r=2 cm, h=3 cm drdt=0.1 cm/min dhdt=−0.2 cm/min V=πr2h Differentiating both sides dVdt=π(r2dhdt+2rdrdth)      =πr(rdhdt+2drdth)       =πr(r(−0.2)+2h(0.1))      =πr5(−r+h) Thus, when r=2 and h=3, dVdt=π(2)5(−2+3)=2π5cm3/minMathematics

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