Compute the surface area?

Question

Compute the surface area of the portion of the cone z=sqrt(x^2+y^2) below the plane z=4. (Answer: 16pi*sqrt(2))

Answer 1

You can use geometry to get the answer.

r = 4, h = 4

slant height = sqrt(r^2 + h^2) = 4sqrt(2)

lateral area of a cone

= (1/2)perimeter of the base * slant height

= (1/2) (2pi*4) (4sqrt(2)) = 16pi*sqrt(2)