Solve the problem.
-A spherical tank of water has a radius of $13 \mathrm { ft }$, with the center of the tank $50 \mathrm { ft }$ above the ground. How much work will it take to fill the tank by pumping water up from ground level? Assume the water weighs $62.4 \mathrm { lb } / \mathrm { ft } 3$. Give your answer to the nearest $\mathrm { ft } \cdot \mathrm { lb }$.
A) 14,356,324 ft · lb
B) 35,890,811 ft · lb
C) 28,712,649 ft · lb
D) 9,139,520 ft · lb

Question

Quizplus · Accepted Answer

The volume of the spherical tank is $\frac {4}{3}\pi(13)^3 \approx 9202.62$ cubic feet. The water inside weighs $9202.62$ cubic feet $\cdot 62.4$ pounds per cubic foot = $574383.91$ pounds. To pump it all to a height of $50$ feet above ground level, we need to do work equal to $$574{,}383.91 	ext{ pounds} \cdot 50 	ext{ feet} = 28{,}719{,}195 	ext{ ft }\cdot 	ext{ lb}.$$ To the nearest foot-pound, the answer is $\boxed{	extbf{(C) } 28{,}712{,}649 	ext{ ft} \cdot 	ext{ lb}}$.

Solve the Problem 13ft13 \mathrm { ft }13ft , with the Center of the Tank

Solve the Problem $13 \mathrm { ft }$ , with the Center of the Tank