Math Challenges

Submissions for Problem #24

Problem #24

A cylindrical water tank has height 10 meters and a base radius of 3 meters. If the tank is full of water, how much work is required to pump the water out through the top? (Recall weight density of water is 1000*9.8 = 9800 N/m^3)

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zapwai
Solution:
\( 9800\int_0^{10}\left(10-y\right)9\pi dy=4,410,000\pi\text{ joules} \)
Explanation:
Since each slice has constant area, we could also simply take the entire volume of the water and multiply by the average distance 5 meters.
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