Q1) Q2) water in a vertical cylindrical tank of height 13 ft and radius 2 ft is

Question

Q1)

Q2)

water in a vertical cylindrical tank of height 13 ft and radius 2 ft is to be pumped out. The density of water is 62.4 lb/ ft (a) The tank is full of water and all of the water is to be pumped over the top of the tank. Find the approximate work for the slice as shown. Use Delta or A from the CalcPad. Leave T in your answer. Find the endpoints for the integral that is needed to find the exact amount of work. Lower endpoint Upper endpoint (b) The tank is full of water and all but 3 ft of water will be pumped to a height 4 ft above the top of the tank. Find the approximate work for the slice as shown. Use Delta or A from the CalcPad. Leave T in your answer. Find the endpoints for the integral that is needed to find the exact amount of work. Lower endpoint Upper endpoint

Explanation / Answer

1

a.)

approximate work for the slice = (dm)gh = 62.4(pie)(22)Delta(y)g(13-y) = 249.6*pie*g*(13-y)*Delta(y)

Since the tank is full

Lower end point = 0

upper end point = 13

b.)

approximate work for the slice =(dm)gh = 62.4(pie)(22)Delta(x)g(x+4) = 249.6*pie*g*(x+4)*Delta(x)

Since the tank is 3ft water

Lower end point = 0

upper end point = 3

2.

a.)

r/h = 2/4 = 1/2

Volume of the slice = pie(r2)Delta(h) = pie(h/2)2Delta(h) = (pie*h2/4)Delta(h) = 0.25(pie*h2)Delta(h)

Displacement of slice = 8-h

b.)

Since water is filled upto a depth of two

Lower end point of h = 0

upper end point of h = 2

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