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 = (x^2)h cm^3. 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.

asked by Gary

9 years ago

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1 answer

just use the product rule

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

Now just plug in the given values.

answered by Steve

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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 = (x^2)h cm^3. 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.

1 answer

just use the product rule

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

Now just plug in the given values.

Steve · Answer

just use the product rule v = x^2 h dv/dt = 2xh dx/dt + x^2 dh/dt Now just plug in the given values.