# Calculus

posted by .

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?

• Calculus -

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

• Calculus -

Thank you!

• Calculus -

Where did you get 8 from?

## Similar Questions

1. ### AP Calculus

Sand pouring from a chute forms a conical pile whose height is always equal to the diameter. If the height increases at a constant rate of 5 ft/min, at what rate is sand pouring from the chute when the pile is 10 ft high?
2. ### calculus

Sand falls from a conveyor belt at a rate of 20 m^3/min onto the top of a conical pile. The height of the pile is always 3/4 of the base diameter. Answer the following. a.) How fast is the height changing when the pile is 10 m high?
3. ### calculus

grain is being poured through a chute at rate of 8 ft^3/min and forms a conical pile whose radius of the bottom is always 1/2 the height of pile. How fast is circumference increasing when the pile is 10 feet high?
4. ### CALCULUS

A pile of sand in the shape of a cone whose base diameter is 4 times its height is being built up at 12 pi m3/min. How fast is the height of the pile increasing 3 min after the pouring begins.
5. ### CALCULUS

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 …
6. ### Timerate problem(calculus)

Sand is being dropped at the rate 10 metercube/min onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the increasing when the pile is 8 m high?
7. ### Calculus

Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing …
8. ### Calculus 1

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing …
9. ### Calculus 1

sand is being poured onto the ground forming a conical pile whose height equals 1/4 of the diameter of the base. The sand is falling at a rate of 20cm^3/sec. How fast is the height of the sand pile increasing when it is 3cm high?
10. ### Calculus 1

sand is being poured onto the ground forming a conical pile whose height equals 1/4 of the diameter of the base. The sand is falling at a rate of 20cm^3/sec. How fast is the height of the sand pile increasing when it is 3cm high?

More Similar Questions