$\text { An ornamental light bulb is designed by revolving the graph of } y = \frac { 1 } { 3 } x ^ { \frac { 1 } { 2 } } - x ^ { \frac { 3 } { 2 } }$

Multiple Choice

$\text { An ornamental light bulb is designed by revolving the graph of } y = \frac { 1 } { 3 } x ^ { \frac { 1 } { 2 } } - x ^ { \frac { 3 } { 2 } }$ about the x-axis where x and y are measured in feet. Approximate the amount of glass needed to make the bulb. (Assume that the glass is 0.016 inches thick.) Round your answer to four decimal places.

A) $0.2681 \mathrm { in. } ^ { 3 }$
B) $0.0019$ in. $^ { 3 }$
C) $3.217$ in. $^ { 3 }$
D) $0.0223$ in. $^ { 3 }$
E) $16.7552$ in. $^ { 3 }$