Solve the Problem $\mathrm { y } = 5 \mathrm { x } ^ { 2 } , 0 \leq \mathrm { x } \leq 2$

Multiple Choice

Solve the problem.
-A tank is designed by revolving the parabola $\mathrm { y } = 5 \mathrm { x } ^ { 2 } , 0 \leq \mathrm { x } \leq 2$ , about the $\mathrm { y }$ -axis. The tank, with dimensions in meters, is filled with water weighing $9800 \mathrm {~N} / \mathrm { m } ^ { 3 }$ . How much work will it take to empty the tank by pumping the water to the tank's top? Give your answer to the nearest $\mathrm { J }$ .

A) 256,563 J
B) 8,210,029 J
C) 1,642,006 J
D) 24,630,086 J