Question

8 : sand pouring from a chute forms a conical pile whose height is always equal to the diameter. if the height increases at a constant rate of 5 feet per minute, at what rate is the sand pouring from the chute when the pile is 10 feet high?

Answer 1

When the pile is 10 feet high, the rate at which sand is released from the chute is 125$\pi$ 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$\pi r^{2} h$

v= 1/3$\pi$(x/2)^2(x/2)

v= 1/3$\pi$(x^2/4)(x/2)

v= $\pi$x^3/12

When we translate the height and radius values into terms of x, we obtain:

dv/dt =1/3 $\pi$(3x^2)dx/dt

By solving the equation,

dv/dt =125 $\pi$

Consequently, 125$\pi$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

#SPJ4