A water tank is has the charge of an inverted circular cone of radius 6 feet and

Question

A water tank is has the charge of an inverted circular cone of radius 6 feet and a height 12 feet. The tank is full of water. If the water level is falling at a rate of 2 ft/min, how fast is the tank losing water when the water is 8 feet deep? A beant is being towed by a rope that goes from the bean to a pulley on a dock. The pulley is 5 feet above the point on the boat where the pope is attached to the boat. The rope is being pulled in at a rate of 2 ft/sec. Find the rate at which the beat is approaching the dock when the boat is 12 feet from the dock.

Explanation / Answer

4)radius r=6 ft , height h =12ft

r/h =6/12

r =(1/2)h

volume of cone V =(1/3) r2 h

V =(1/3) ((1/2)h)2h

V =(1/12)h3

differentiate with respect to time t

dV/dt =(1/12)3h2(dh/dt)

dV/dt =(1/4)h2(dh/dt)

water level falling at rate of 2ft/min when water is 8 feet deep =>h =8 ,dh/dt =-2

dV/dt =(1/4)82(-2)

dV/dt =-32

tank is losing water at rate of 32 =100.53 cubic feet /min

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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