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

The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve $z = \frac { 1 } { 5 } y ^ { 2 } + 2 , ( 0 \leq y \leq 5 ) \text { in the } y z \text {-plane about }$ the z-axis. All measurements are in centimeters and the bushing is set on the xy-plane. Use the shell
Method to find its volume. Round your answer to one decimal place.

A) $392.7 \mathrm {~cm} ^ { 3 }$
B) $39.3 \mathrm {~cm} ^ { 3 }$
C) $52.4 \mathrm {~cm} ^ { 3 }$
D) $196.3 \mathrm {~cm} ^ { 3 }$
E) $8.3 \mathrm {~cm} ^ { 3 }$