Question

Sands falls off a conveyor belt onto the ground at a steady rate of 200cm^3 per second forming a conical pile whose height always equal to half the diameter of the base, at what rate is the height increasing after 10 second

Answer 1

height of cone is 1/2 the diameter
---> height of cone equals its radius

V= (1/3)π r^2 h, but r = h
V = (1/3) π h^3
dV/dt = π h^2 dh/dt ***

dV/dt = 200 cm^3/s
so when t = 10
V = 2000 cm^3
2000 = (1/3)π h^3
h^3 = 6000/π
h = (6000/π)^(1/3) = appr 12.407

in ***
200 = π(12.407)^2 dh/dt
dh/dt = 200/(π(12.407)^2) = appr .414 cm/sec

check my arithmetic