The rate of change in position at a given point in time
1 answer:
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Answer:
The water required to pump all the water to a platform 2 feet above the top of the pool is is 6061310.32 foot-pound.
Explanation:
Given that,
Radius = 21 feet
Height = 10 feet
Weighing = 62.5 pounds/cubic
Work = 4329507.37572
Height = 2 feet
Let's look at a horizontal slice of water at a height of h from bottom of pool
We need to calculate the area of slice
Using formula of area
Put the value into the formula
Thickness of slice
The volume is,
We need to calculate the force
Using formula of force
Where, W = water weight
V = volume
Put the value into the formula
We need to calculate the work done
Using formula of work done
Put the value into the formula
We do this by integrating from h = 0 to h = 10
We need to find the total work,
Using formula of work done
Put the value into the formula
To pump 2 feet above platform, then each slice has to be lifted an extra 2 feet,
So, the total distance to lift slice is (12-h) instead of of 10-h
We need to calculate the water required to pump all the water to a platform 2 feet above the top of the pool
Using formula of work done
Put the value into the formula
Hence, The water required to pump all the water to a platform 2 feet above the top of the pool is is 6061310.32 foot-pound.