Question

Sand is poured onto a level piece of ground at the rate of 0.25 m^3/min and forms a conical pile whose height is equal to its base diameter. How fast is the height increasing at the instant when the height is 0.50 m? V = 1/3(pi)(r^2)h

I got 3/pie, is that correct?

Answer 1

I got 4/π

let the radius be r, then the height is 2r
V= (1/3)πr^2 h
= (1/3)πr^2(2r)
= (2/3)πr^3
dV/dt = 2π r^2 dr/dt
when 2r=.5
r = .25 and dV/dt = .25

1/4 = 2π(1/16) dr/dt
times 8
2 = π dr/dt
dr/dt = 2/π
d(2r)/dt = d(height)/dt = 4/π

Answer 2

Thank you!

Answer 3

Where did you get 8 from?