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

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 $y = \frac { 1 } { 2 } x ^ { 2 }$ and the line $y = \frac { 1 } { 2 }$ from $x = - 1$ to $x = 1$ . The pool is $10 \mathrm { ft }$ by $20 \mathrm { ft }$ and $8 \mathrm { ft }$ deep. If the drain plate is designed to withstand a fluid force of $200 \mathrm { lb }$ , how high can the pool be filled without exceeding this limitation?

A) 5 ft 1 in.
B) 5 ft 6 in.
C) 5 ft 9 in.
D) 4 ft 11 in.