the volume of a rectangular box with a square base remains constant at 500 cm^3 as the area of the box increases at a rate of 3cm^2/sec. find the rate at which the height of the box is decreasing when each side of the base is 18 cm long.

Answer 1

500=areabase* h

take the derivative.

0=d areabase/dt * h+ areabase*dh/dt

solve for dh/dt when
areabase=18^2
h= 500/18^2
dareabase/dt=3 cm^2/sec