Use the Disk or Shell Method to Find the Volume $x ^ { \frac { 2 } { 3 } } + y ^ { \frac { 2 } { 3 } } = 7 ^ { \frac { 2 } { 3 } }$

Multiple Choice

Use the disk or shell method to find the volume of the solid generated by revolving the region in the first quadrant bounded by the graph of the equation about the given line.
$x ^ { \frac { 2 } { 3 } } + y ^ { \frac { 2 } { 3 } } = 7 ^ { \frac { 2 } { 3 } }$
(i) the $x$ -axis; (ii) the $y$ -axis

A)
(i) $\frac { 1,568 } { 15 } \pi$ ; (ii) $\frac { 1,568 } { 15 } \pi$
B)
(i) $\frac { 686 } { 25 } \pi$ ; (ii) $\frac { 1,568 } { 15 } \pi$
C)
(i) $\frac { 1,568 } { 15 } \pi$ ;(ii) $\frac { 392 } { 15 } \pi$
D)
(i) $\frac { 2,744 } { 25 } \pi$ ;(ii) $\frac { 2,744 } { 25 } \pi$
E)
(i) $\frac { 392 } { 15 } \pi$ ;(ii) $\frac { 1,568 } { 15 } \pi$