Question

求解一道AP微积分题!Gravel is being dumped from a conveyor belt at a

Answer 1

let h be the height,the volume of the right cirular cone is:

S = 1/3 pi r^2 h = 1/3 pi (h/2)^2 h = pi h^3 /12

dS/dt = pi h^2/4 * dh/dt = 20

so dh/dt = 20 *4 /( pi h^2)

when h=12,dh/dt = 80/(pi * 12^2) = 5/(9pi) feet / min