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Find the rate of change of the volume of a cone with respect to time, given the formula V = (1/3)πr^2h, when dr/dt is a litchi per minute, and dh/dt is in units per minute.

User Ron Kalian
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1 Answer

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Final answer:

The rate of change of the volume of a cone with respect to time is calculated by differentiating the volume formula and substituting the given rates of change for the radius and height.

Step-by-step explanation:

The question at hand involves calculus, specifically related to the rate of change of the volume of a cone with respect to time. To solve this, one would use the given formula for the volume V of a cone, which is V = (1/3)πr^2h, and apply the chain rule to differentiate both sides with respect to time (t).

The rate of change of the volume with respect to time, represented as dV/dt, can be found by differentiating the volume formula:

dV/dt = πr^2(dh/dt)/3 + 2πrh(dr/dt)/3

This formula incorporates the given rates of change of both the radius (dr/dt, in litchis per minute) and the height (dh/dt, in units per minute) to find the final rate at which the volume changes over time.

User Tsvikas
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