Question

A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by V = x2h cm3. Find the rate at which the volume of the box is changing when the edge length of the base is 10 cm, the edge length of the base is increasing at a rate of 3 cm/min, the height of the box is 5 cm, and the height is decreasing at a rate of 1 cm/min.

Answer 1

v = x^2 h

now use the product rule and chain rule:

dv/dt = 2xh dx/dt + x^2 dh/dt

Now just plug in your numbers

Answer 2

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