Find the surface area of the surface S.
-$\mathrm { S }$ is the paraboloid $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } - \mathrm { z } = 0$ below the plane $\mathrm { z } = 2$.
A) $\frac { 13 } { 6 } \pi$
B) $\frac { 9 } { 2 } \pi$
C) $\frac { 13 } { 3 } \pi$
D) $\frac { 13 } { 2 } \pi$

Question

Quizplus · Accepted Answer

The surface area of the paraboloid $x^2 + y^2 = z$ below $z = 2$ is calculated using a surface integral in cylindrical coordinates, resulting in $\frac{13}{3} \pi$.

Find the Surface Area of the Surface S S\mathrm { S }S

Find the Surface Area of the Surface S $\mathrm { S }$