Find the Area of the Surface Generated by Revolving the Curve

Multiple Choice

Find the area of the surface generated by revolving the curve about the given axis. $x = t , y = 6 t , 0 \leq t \leq 9$
(i) $x$ -axis; (ii) $y$ -axis

A) (i) $486 \sqrt { 37 } \pi$ ; (ii) $81 \sqrt { 37 } \pi$
B) (i) $324 \sqrt { 82 } \pi$ ; (ii) $36 \sqrt { 82 } \pi$
C) (i) $486 \sqrt { 37 } \pi$ ; (ii) $36 \sqrt { 37 } \pi$
D) (i) $81 \sqrt { 37 } \pi$ ; (ii) $486 \sqrt { 37 } \pi$
E) (i) $324 \sqrt { 37 } \pi$ ; (ii) $81 \sqrt { 37 } \pi$