# calculus

sand is being dropped onto a conical pile in such a way that the height of the pile is always twice the base radius.what is the rate of change of the volume of the pile with respect to the radius when the radius of the pile is 12 inches?

1. 👍 0
2. 👎 0
3. 👁 93
asked by raye
1. you need dV/dr
V = (1/3) pi r^2 (2r) = (2/3) pi r^3
dV/dr = (2/3)pi * 3 r^2
= 2 pi r^2
when r = 12
dV/dr = 288 pi

1. 👍 0
2. 👎 0
posted by Damon

## Similar Questions

1. ### Related rates

Sand is being dropped at the rate of 10 cubic meter per minute onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the height increasing when the pile is 8 meters high?

asked by :) on May 14, 2012
2. ### 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?

asked by Mike on October 6, 2014
3. ### 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?

asked by ben on September 10, 2016
4. ### 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?

asked by Khan on September 10, 2016
5. ### Related Rates

Sand is falling into a conical pile at the rate of 10 m3/sec such that the height of the pile is always half the diameter of the base of the pile. Find the rate at which the height of the pile is changing when the pile is 5 m.

asked by Dimple on January 23, 2016
6. ### calculus

please help if you can At a sand & gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 16 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what

asked by kim on October 14, 2010
7. ### Calculus

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 6 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of

asked by Anonymous on March 8, 2017
8. ### Time rates

sand is being dragged at the rate of 10m^3/min into a conical pile. if the height of the pile is always twice the base radius, at what rate is the height increasing when the pile is 2m high?

asked by Anonymous on June 16, 2017
9. ### Calculus

Sand falls from a conveyor belt onto a conical pile at a rate of 6ft/mi^3. The radius of the base is always equal to two-thirds of the pile’s height. At what rate is the height of the pile changing when the radius of the base of

asked by Jace on July 3, 2016
10. ### calculus

At a quarry, sand is filling off a conveyor onto a conical pile at a rate of 15 cubic feet per minute. The diameter of the base of the cone is four times the height. At what rate is the height of the pile changing when the pile is

asked by peter on March 15, 2012

More Similar Questions