A Surface Has the Shape of the Cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$

question 120

Multiple Choice

A surface has the shape of the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ between $z = 0$ and $z = 1$ with the density function $\rho ( x , y , z ) = 1 - z$ . Find the mass of the surface.

• A) \(\sqrt { 2 } \pi\)
• B) \(\frac { \sqrt { 2 } \pi } { 3 }\)
• C)\(6\)
• D)\(1\)
• E)\(2 \sqrt { 2 } \pi\)
• F)\(2 \pi\)
• G)\(\frac { 2 \sqrt { 2 } \pi } { 3 }\)
• H)\(0\)

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