Conveyor Belt Cone

Question

Sand falls from a conveyor belt at the rate of 30 cubic feet per minute onto the top of a conical pile. The height of the pile is always equal to the base diameter. At what rate is the height of the pile increasing at the instant the height is 10 feet.

a.6/5π

b.6/5

c.6/π

d.1/5π

e.3/5π

f.3/5

g.2/5π

Answer 1

Your answer is a

If V= cone volume, r = radius of the base of the cone, h = height of the cone, t = time

The volume of the cone is (pi)r²h/3 we know that h = 2r So volume is (pi)h³/12

When you differentiate, you get dV/dt = (1/4)(pi)h² dh

dh = 10, dv/dt = 30 When you plug in the numbers, you get the desired result!