Question

Sand is being poured from a converyer belt forming a conical pile whose base diameter is eual to its height at all times. If the base diameter is inreasing at 2 m/min when the base is 2 m wide. How fast is the sand being poured onto the pile?

Answer 1

given: 2r = h

d(diameter)/dt = 2 m/min
d(2r)/dt = 2 m/min
d(r)/dt = 1 m/min

V(ofcone) = (1/3)πr^2 h
= (1/3)πr^2 (2r)
= (2/3)π r^3

dV/dt = 2πr^2 dr/dt
= 2π(1^2)((1)

= 2π m^3/min