# Sand pouring from a chute forms a conical pile whose height is always equal to the diameter.. If the height increases at a rate of 5ft per/min, at what rate is the sand pouring from the chute...

Sand pouring from a chute forms a conical pile whose height is always equal to the diameter..

If the height increases at a rate of 5ft per/min, at what rate is the sand pouring from the chute when it is 10 ft high?

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Expert Answers

jeew-m | Certified Educator

The rate of sand increasing height = 5ft/min

The time required to fill 10 ft height = 10/5 min = 2min

When the height of the sand is 10ft then the diameter of the sand is also 10ft.

Volume of a cone `= 1/3*pi*r^2*h` with standard notations.

Volume of sand filled `= 1/3*pi*(10/2)^2*10 ft^3 = 261.8 ft^3`

This volume is filled in 2 minutes.

Rate of the sand pouring from chute `= 261.8/2 ft^3/s = 130.9f^3/s`

*So the rate of the sand pouring from chute is 130.9 cubic feet per second.*