Find the Area of the Part of the Cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$

Multiple Choice

Find the area of the part of the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ that is cut off by the cylinder $( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$

A) $9 \pi \sqrt { 2 }$
B) $3 \pi \sqrt { 2 }$
C) $2 \pi \sqrt { 2 }$
D) $4 \pi \sqrt { 2 }$