
True or False ? Justify your answer with a proof or a counterexample.
435. The amount of work to pump the water out of a halffull cylinder is half the amount of work to pump the water out of the full cylinder.

To check: whether the statement, “The amount of work to pump the water out of a half-full cylinder is half the amount of work to pump the water out of the full cylinder” is true or false.
Answer to Problem 435RE
The given statement is false.
Explanation of Solution
Given information:
The given statement is, “The amount of work to pump the water out of a half-full cylinder is half the amount of work to pump the water out of the full cylinder”.
Calculation:
Consider a cylinder of radius
Let
So, the work done to empty the completely filled cylinder is given by,
If the cylinder is half filled, then the work done to empty the half-filled cylinder is given by
Thus,
Therefore, the amount of work to pump the water out of a half-full cylinder is three-fourth the amount of work to pump the water out of the full cylinder.
Conclusion:
Hence, the given statement is false.
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