Calculate the work required to pump water into the tank shown below, through a hole at the base of the tank. The water source is at ground level.
Hint: Density of water \( =62.4 \mathrm{lb} / \mathrm{ft}^{3} \).
Round your answer to the nearest whole number.
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Answer

\(W = 62.4 \int_0^h (h - y)\frac{y^2}{h^2}\pi \, dy \)

Steps

Step 1 ：\(V = \frac{1}{3}\pi h r^2 \)

Step 2 ：\(W = \rho \int_0^h (h - y)A(y) \, dy \)

Step 3 ：\(W = 62.4 \int_0^h (h - y)\frac{y^2}{h^2}\pi \, dy \)