An inverted conical tank has a height of 10 ft and a top radius of 5 ft

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

An inverted conical tank has a height of 10 ft and a top radius of 5 ft. At the instant when the water depth is 4 ft, water is draining from the tank at a rate of

4\text{ ft}^3/\text{min}

. Find both of the following instantaneous rates at that moment: • the rate at which the water depth

h

is changing (

\mathrm d h/\mathrm dt

), and • the rate at which the radius

r

of the water surface is changing (

\mathrm d r/\mathrm dt

). Assume the water surface remains similar in shape to the tank.

Related theory

Related Rates
Rates of change
Rate of change of quantities

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