A trough is 12 ft long and its ends have the shape of isosceles traingles that a

Question

A trough is 12 ft long and its ends have the shape of isosceles traingles that are 2 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 15 ft^3/min, how fast is the water level rising when the water is 8 inches deep? Water is leaking out of an inverted conical tank at a rate of 10,500cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 600 cm and the diameter at the top is 400cm. If the water level is rising at a rate of 20 cm/min when the height of the water is 200 cm. find the rate at which water is being pumped into the tank.(Round your answer to the nearest integer.)

Explanation / Answer

9)let distance between ends of top of trough be b , height be h

volume of trough v=(1/2)*b*h*12

v=6bh

given ends are 2 ft across top and height is 1ft

b/h=2/1

=>b=2h

volume of trough v=6*2h*h

volume of trough v=12h2

given water is 8 inches deep=>h =8*(1/12) =2/3 ft

volume of water in trough increasing at 15ft3/min=>dv/dt =15

v=12h2

differentiate with repect to t

dv/dt=12*2h dh/dt

15=12*2*(2/3)*dh/dt

15=16dh/dt

dh/dt=15/16

dh/dt=0.9375ft/min

waterlevel rising at 0.9375ft/min

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