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
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
Consequently, 125ft^3/min of sand per minute are being released from the chute.
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