The Top of a Rubber Bushing Designed to Absorb Vibrations $z = \frac { 1 } { 5 } y ^ { 2 } + 3 , ( 0 \leq y \leq 5 ) \text { in the } y z \text {-plane }$

Multiple Choice

The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve $z = \frac { 1 } { 5 } y ^ { 2 } + 3 , ( 0 \leq y \leq 5 ) \text { in the } y z \text {-plane }$ about the z-axis. The bushing has a hole of 4 centimeters in diameter through its center and parallel to the axis of revolution. All measurements are in centimeters and the bushing is set on the xy-plane. Find the volume of the rubber bushing. Round your answer to two decimal places.

A) $22.05 \mathrm {~cm} ^ { 3 }$
B) $146.08 \mathrm {~cm} ^ { 3 }$
C) $183.78 \mathrm {~cm} ^ { 3 }$
D) $355.00 \mathrm {~cm} ^ { 3 }$
E) $138.54 \mathrm {~cm} ^ { 3 }$