Write a Set of Parametric Equations for the Surface of Revolution

Multiple Choice

Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function $y = x ^ { \frac { 3 } { 7 } } , 0 \leq x \leq 4$ about the $x$ -axis.

A) $x = u ^ { \frac { 3 } { 7 } } , y = u ^ { \frac { 3 } { 7 } } \cos v , z = u ^ { \frac { 3 } { 7 } } \sin v , 0 \leq u \leq 4,0 \leq v \leq 2 \pi$
B) $x = u , y = u ^ { \frac { 3 } { 7 } } \cos v , z = u ^ {\frac { 3 } { 7 } } \sin v , 0 \leq u \leq 4,0 \leq v \leq 2 \pi$
C) $x = u , y = u ^ { \frac { 3 } { 7 } } \sin v , z = u ^ { \frac { 3 } { 7 } } \cos v , 0 \leq u \leq 4 , v \geq 0$
D) $x = u ^ { \frac { 3 } { 7 } } , y = u ^ { \frac { 3 } { 7 } } \sin v , z = u ^ { \frac { 3 } { 7 } } \cos v , u \geq 4,0 \leq v \leq 2 \pi$
E) $x = v , y = v ^ { \frac { 3 } { 7 } } \cos u , z = v ^ { \frac { 3 } { 7 } } \sin u , u \geq 4 , v \geq 0$