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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

A steel tank has the shape of a circular cylinder oriented vertically with diameter 4 m and height 5 m. The tank is currently filled to a level of 3 m with cooking oil that has a density of 920 kg/m3. Compute the work required to pump the oil out through a 1-meter spout at the top of the tank.

To determine

To compute:

The work required to pump the oil out of the tank.

Explanation

1) Given:

Diameter of cylinder is 4m.

Height of cylinder is 5m.

Density of oil is 920kg/m3.

2) Calculations:

The volume of a horizontal slice of cooking oil having x meter thickness is πr2x.

That is,π22x m3=4πx m3

Density of oil is 920kg/m3.

Therefore,

Mass of slice is 920×4πx=3680 πx

Weight is 9.8×3680πx=36064πx  N

Now, the height of the cylinder is 5m, and the height of the spout is 1m, so the total height is 6m.

Also, the cylinder is filled to a level of  3m.

Thus, to calculate the total work needed to empty the tank, integrate the weight from 3m  to 6m

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