A closed cylindrical storage tank contains a non-reactive liquid

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A closed cylindrical storage tank contains a non-reactive liquid. For mechanical reasons, the volume of the tank is designed to remain constant at

240\pi\text{ m}^3

even while the radius

r

of the tank slowly decreases because of external pressure. At an instant when the radius is

4.0\text{ m}

and decreasing at

0.015\text{ m/s}

, the tank’s height

h

is changing to preserve the fixed volume. (1) Find the instantaneous rate of change

\dfrac{dh}{dt}

of the height at this instant. State your answer with correct sign and units. (2) Determine the instantaneous rate of change of the lateral surface area

S=2\pi r h

at this same instant. (3) Is the lateral surface area increasing or decreasing? Explain your reasoning based on the sign of

\dfrac{dS}{dt}

Related theory

Rates of Change
Related Rates
Rate of change of quantities

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