The question is to derive the surface area of a cone.
slant= square root ( r^2 + h^2)
surface area= int int [square root(fx^2 + fy^2 +1) da]
surface area of cone side= pi *r(r^2+h^2)
3d cone formula: z= h/r(squareroot x^2+y^2)
The Attempt at a Solution
by looking at the structure I know that it is the area of the base (circle) + the area of the slant/side, but when I solve for the surface area using double integrals I'm stuck w/ squareroot 2 in the formula. How can I cancel that out?
i calculated fx as hx/rsqareroot(x^2+y^2)
and fy as hy/rsquareroot(x^2+y^2)
i plugged that into the formula for surface area and got: int int [h/r squareroot(2)] r dr [email protected]
it feels like it isn't right and I don't know how to cancel the sqareroot(2) during integration. Can someone hint me in the right direction?