Sand is poured onto a surface at 13 cm3/sec, forming a conical pile whose base diameter is always equal to its altitude. how fast is the altitude of the pile increasing when the pile is 1 cm high? note that the volume of a cone is 13πr2h where r is the radius of the base and h is the height of the cone.

Altitude of the pile will increase by 16.56 cm per second.

Step-by-step explanation:

Sand is poured onto a surface at the rate = 13 cm³ per second

Or

It forms a conical pile with a diameter d cm and height of the pile = h cm

Here d = h

Volume of the pile cm³per sec.

Since h = d = 2r [r is the radius of the circular base]

r =

Since cm³per sec.

13 = [For h = 1 cm]

cm per second.

Therefore, altitude of the pile will increase by 16.56 cm per second.

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step-by-step explanation:

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