A reservoir has the shape of a truncated cone as shown in the gure above. It measures
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Question:
A reservoir has the shape of a truncated cone as shown in the gure above. It measures m high. The radius of the base is m and the top radius is m It is lled with water. We want to calculate the amount of work required to pump all of its water through the hose standing m above the reservoir.
i Let x be the height in metres measured from the base of the reservoir. The weight of a thin water layer between heights x and xDelta x is approximately PxDelta x What is Px
Px
FORMATTING: Express the answer as a function of x
Recall that the density of water is rho Kgm and the acceleration due to gravity on the earths surface is gms
ii The work in Joules required to pump the thin water layer to m above the reservoir is approximately wx delta x What is wx
wx
FORMATTING: Express the answer as a formula
iii Using previous results, determine the amount of work required to pump all of the water to m above the reservoir.
FORMATTING: If you round your answer, ensure that the round off error is less than of the value.
Work Joules
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