Question

Find the surface area, A(S), of the upper half of a cone defined parametrically by the position vector r(s,t)=⟨scost,ssint,s⟩, where 0≤s≤1,0≤t≤2π.

Answer 1

The surface area of the upper half of a cone can be found using a surface integral. Plug in the given position vector and limits of integration to calculate the surface area.

Step-by-step explanation:

The position vector r(s,t) = ⟨scost, ssint, s⟩ defines a cone. To find the surface area of the upper half of the cone, we need to find the surface integral. In this case, the surface integral can be written as A(S) = ∬√(1 + (dr/ds)² + (dr/dt)²) ds dt. Plugging in the given position vector and the limits of integration, the surface area can be calculated.