When the pile is 10 feet high, the rate at which sand is released from the chute is 125
ft^3/min
Let x denote the cone's height.
We've been told that when sand is poured down a chute, it always creates a conical pile whose height is equal to its diameter.
Since radius is known to be equal to half of diameter, the radius of a cone would be x/2.
To resolve the issue at hand, we shall use the volume of cone formula.
v=1/3![\pi r^{2} h](https://tex.z-dn.net/?f=%5Cpi%20r%5E%7B2%7D%20h)
v= 1/3
(x/2)^2(x/2)
v= 1/3
(x^2/4)(x/2)
v=
x^3/12
When we translate the height and radius values into terms of x, we obtain:
dv/dt =1/3
(3x^2)dx/dt
By solving the equation,
dv/dt =125 ![\pi](https://tex.z-dn.net/?f=%5Cpi)
Consequently, 125
ft^3/min of sand per minute are being released from the chute.
To learn more about volume of cone click here:
brainly.com/question/1578538
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