A Swimming Pool Is Circular with A $20 - \mathrm { ft }$

Multiple Choice

A swimming pool is circular with a $20 - \mathrm { ft }$ diameter. The depth is constant along east-west lines and increases linearly from $3 \mathrm { ft }$ at the south end to $9 \mathrm { ft }$ at the north end. Find the volume of water in the pool.

A) $610 \pi \mathrm { tt } ^ { 3 }$
B) $800 \pi \mathrm { tt } ^ { 3 }$
C) $700 \pi \mathrm { tt } ^ { 3 }$
D) $900 \pi \mathrm { tt } ^ { 3 }$
E) $600 \pi \mathrm { tt } ^ { 3 }$