The radius of a right circular cylinder increases at the rate of 0.2 c m / sec and the height decreases at the rate of 0.1 c m / sec . The rate of change of the volume of the cylinder when the radius is 1 c m and the height is 2 c m is

Question

The radius of a right circular cylinder increases at the rate of 0.2 c m / sec and the height decreases at the rate of 0.1 c m / sec . The rate of change of the volume of the cylinder when the radius is 1 c m and the height is 2 c m is, π 10 c m 3 / s e c, 9 π 10 c m 3 / s e c, 7 π 10 c m 3 / s e c, π 5 c m 3 / s e c

MARKS App · Accepted Answer

Volume of cylinder, V = π r 2 h d V d t = π r 2 d h d t + 2 r h d r d t Given, d h d t = - 0.1 , d r d t = 0.2 d V d t = π - 0.1 1 2 + 2 1 2 0.2 d V d t = π - 1 10 + 4 5 = 7 π 10 cm 3 / sec

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