Question

Wheat is poured through a chute at the rate of 10 ft^3/min and falls in a cone-shaped pile whose bottom radius is always half its height. How fast is the height of the cone increasing when the pile is 8 feet high?
Volume of a cone=1/3(pi)r^2h

Answer 1

R=1/2h Assume the water in cone is at height,h and radius is r.V=1/3Pi(1/2h)^2(h) V=1/12(Pi)h^3. by differentiating V:dV/dt=1/4(pi)h^2dh/dt 10=1/4*3.142*8^2dh/dt dh/dt=10/50.27=0.199ft/min