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Marcos Domingues

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## Homework Statement

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I have this expression: dV/dt = F0 - K*h^(1/2); it describes a variation in time of a fluid volume V in a cone-shaped tank of total volume H*pi*R²/3;

By a trigonometric relation we get V = (pi*R²/3*H²)*h³; since tan a = H/R = h/r

where: R = radius of the tank; H = height of the tank; h = variable height of the fluid; r = radius related to a specific height h

So, when we replace V, we got the general expression (pi*R²/3*H²) d(h³)/dt = F0 - K*h^(1/2);

This d(h³) term is the main problem on the integration. How do I integrate this expression?

## Homework Equations

(pi*R²/3*H²) d(h³)/dt = F0 - K*h^(1/2)

## The Attempt at a Solution

Maybe consider d(h³) = dh*dh*dh and solve it as multiple integrals?

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