The side length of a rectangular box with a square base is increasing at the rate of 2 ft/sec, while the height is decreasing at the rate of 2 ft/sec. At what rate is the volume of the box changing when the side length is 10 ft and the height is 12 ft? Remember to use the product rule when you find the expression for dV,dt.

Question

The side length of a rectangular box with a square base is increasing at the rate of 2 ft/sec, while the height is decreasing at the rate of 2 ft/sec. At what rate is the volume of the box changing when the side length is 10 ft and the height is 12 ft? Remember to use the product rule when you find the expression for  dV,dt.

E · Accepted Answer

Just give the answer Steve

Steve · Answer

so, did you use the product rule as advised? v = x^2 h dv/dt = 2xh dx/dt + x^2 dh/dt Now just plug in your values to find dv/dt. Note that dv/dt does not actually depend on h at all, just dh/dt.