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 cm 3 / min ,

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 cm 3 / min , when the radius is 2 cm and the height is 3 cm is

TestHub · Accepted Answer

Given V = π r 2 h . Differentiating both sides, we get d t d V ​ = π ( r 2 d t d h ​ + 2 r d t d r ​ h ) = π r ( r d t d h ​ + 2 h d t d r ​ ) d t d r ​ = 10 1 ​ and d t d h ​ = − 10 2 ​ ​ d t d V ​ = π r ( r ( − 10 2 ​ ) + 2 h ( 10 1 ​ ) ) = 5 π r ​ ( − r + h ) Thus, when r = 2 and h = 3 , d t d V ​ = 5 π ( 2 ) ​ ( − 2 + 3 ) = 5 2 π ​

Mathematics - Application of Derivative Question with Solution | TestHub

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