Question

A machine starts dumping sand at the rate of 20 m3/min, forming a pile in the shape of a cone. The height of the pile is always twice the length of the base diameter. After 5 minutes, how fast is the base area of the base increasing?

I honestly have no idea how to start this question

Answer 1

Since the height is twice the diameter, the height is equal to the radius of the circular base.
Let the radius be r
V = (1/3)π r^2 h, but h = r
V = (1/3) π r^3
dV/dt = π r^2 dr/dt
dr/dt = 20/(πr^2) **

when t = 5 min, V = 5(20) = 100 m^3
100 = (1/3)πr^3
300 = πr^3
r^3 = 300/π
r = (300/π)^(1/3) ***

area of base = A = πr^2
dA/dt = 2π r dr/dt
= 2π(***)(**)
= ......

I will let you do the button-pushing

Answer 2

huh? height is twice the diameter, not half h = 4r

Make that change, Nicole, and redo the steps.

Answer 3

thanks Steve