Entered Answer Previeww (2 pts) Gravel is being dumped from a conveyor belt at a

Question

Entered Answer Previeww (2 pts) Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 15 feet high? Recall that the volume of a right circular cone with height h and radius of the base T is given by h feet per minute You have atte Your overall recorded score is 0%. You have unlimited attempts remaining. this ons s as: thML

Explanation / Answer

dV/dt = 30 ft^3/min

Given:
diameter = height
2r = h
r = h/2

Given:
V = (1/3)*pi*r^2*h
V = (1/3)*pi*(h/2)^2*h
V = (1/3)*pi*h^3/4
V = pi*h^3/12
V = (pi/12)*h^3

differentiate with respect to t,
dV/dt = d/dt ((pi/12)*h^3)
dV/dt = (pi/12)*3*h^2 * dh/dt

put values:
30 = (3.14/12)*3*15^2 * dh/dt
30 = 3.14*4*15^2 * dh/dt
30 = 2826 * dh/dt
dh/dt = 0.0106 feet per minute

Answer: 0.0106 feet per minute

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.