Solve the Problem $\mathrm { y } = \frac { 1 } { 2 } \mathrm { x } ^ { 2 }$

Multiple Choice

Solve the problem.
-A rectangular swimming pool has a parabolic drain plate at the bottom of the pool. The drain plate is shaped like the region between $\mathrm { y } = \frac { 1 } { 2 } \mathrm { x } ^ { 2 }$ and the line $\mathrm { y } = \frac { 1 } { 2 }$ from $\mathrm { x } = - 1$ to $\mathrm { x } = 1$ . The pool is $10 \mathrm { ft }$ by $20 \mathrm { ft }$ and $8 \mathrm { ft }$ deep.
If the pool is being filled at a rate of $200 \mathrm { ft } ^ { 3 } / \mathrm { hr }$ , what is the force on the drain plate after 4 hours of filling? Round your answer to two decimal places if necessary.

A) 486.72 lb
B) 166.4 lb
C) 76.96 lb
D) 153.92 lb