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The volume of a conical pile of sand is increasing at a rate of 300πcm3/sec
300π cm^3/sec
. The height (h) of the pile is always four times the radius (r)
Express the radius in centimeters as a function of time in seconds.

Respuesta :

SatCompton
So using the formula for the volume of a cone:
r^2pi x h/3

The height is always 4 times the radius, so:
h=4r

Now putting the values into the original formula:

r^2pi x 4r/3

Now to see how much the radius increases per second:

r^2pi x 4r/3=300pi

r^2 x 4r/3=300

r^2 x 4r=900

r^2 x r=225

r^3=225

The radius increases by the cubic square root of 225 cm per second.

f(s)= 225^1/3 cm