⦁ Sand is being poured on the ground from the office of an elevated pipe. It forms a conical pile whose altitude is always equal to 4/3 the radius of the base. Approximate all the answers to two decimal places.

Question

⦁	Sand is being poured on the ground from the office of an elevated pipe.  It forms a conical pile whose altitude is always equal to 4/3 the radius of the base.  Approximate all the answers to two decimal places.
⦁	How fast is the volume increasing when the radius of the base is 4 feet and is increasing at the rate of 0.01 ft. /s?
⦁	If sand is falling at the rate of 5 cubic ft. / s., how fast is the radius of the pile increasing when the radius is 5 feet?

R_Scott · Accepted Answer

V = 1/3 π r^2 h = 1/3 * π * r^2 * (4 r / 3) = (4 π / 9) * r^3

implicit differentiation ... dV = (4 π / 9) * 3 r^2 dr = (4 π / 3) * r^2 dr

use the equation by plugging in known (given) values and solving