The base of a rectangular tank measures 10 ft by 20 ft. The tank is 16 ft tall, and its top is 10 ft below ground level. The tank is full of water weighing 62.4 lb/ft3. How much work does it take to empty the tank by pumping the water to ground level? Give your answer to the nearest ft ∙ lb.

Question

Mathematics

Lilia Sheppard

28 June, 22:07

The base of a rectangular tank measures 10 ft by 20 ft. The tank is 16 ft tall, and its top is 10 ft below ground level. The tank is full of water weighing 62.4 lb/ft3. How much work does it take to empty the tank by pumping the water to ground level? Give your answer to the nearest ft ∙ lb.

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Answers (1)

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Leandro Mcdonald · Answer 1

2 X 10∧6 ft. lb

Step-by-step explanation:

Volume of rectangular tank = Base area X Height = (10 X 20 X 16) ft³ = 3200ft³

Mass of tank filled with water = 3200ft³ X 62.4 lb/ft³ = 199680lb or 90706.37kg

Hence, work done due to gravity,Δg = m * g * h, where, m = mass of tank, g = gravity = 9.8m/s² and h = height = 10ft or 3.05 meter (m)

∴ Δg = 90706.37 * 9.8 * 3.05 = 2.711 X10∧6 J or 2 X 10∧6 ft. lb