A Tank on the Wing of a Jet Aircraft Is $y = \frac { 1 } { 15 } x ^ { 2 } \sqrt { 2 - x }$

Multiple Choice

A tank on the wing of a jet aircraft is formed by revolving the region bounded by the graph of $y = \frac { 1 } { 15 } x ^ { 2 } \sqrt { 2 - x }$ and the $x$ -axis $( 0 \leq x \leq 2 )$ about the $x$ -axis, where $x$ and $y$ are measured in meters. Find the volume of the tank. Round your answer to two decimal places.

A) $0.45 \mathrm {~m} ^ { 3 }$
B) $0.33 \mathrm {~m} ^ { 3 }$
C) $0.03 \mathrm {~m} ^ { 3 }$
D) $1.79 \mathrm {~m} ^ { 3 }$
E) $0.12 \mathrm {~m} ^ { 3 }$