Consider the parametric surface 𝑆:𝑟⃑(𝑢,𝑣)=〈sin𝑢cos𝑣,sin𝑢sinw
Posted: Tue Jun 07, 2022 8:03 am
Consider the parametric surface
𝑆:𝑟⃑(𝑢,𝑣)=〈sin𝑢cos𝑣,sin𝑢sin𝑣,cos𝑢〉 with 0≤𝑢 ≤ 𝜋/3, 0≤𝑣≤2𝜋.
(a) Find the scalar equation of the tangent plane to 𝑆 at the
point (𝜋
4,𝜋). Answer: −𝑥+𝑧=√2
(b) Find the surface area of 𝑆. Answer: 𝜋
𝑆:𝑟⃑(𝑢,𝑣)=〈sin𝑢cos𝑣,sin𝑢sin𝑣,cos𝑢〉 with 0≤𝑢 ≤ 𝜋/3, 0≤𝑣≤2𝜋.
(a) Find the scalar equation of the tangent plane to 𝑆 at the
point (𝜋
4,𝜋). Answer: −𝑥+𝑧=√2
(b) Find the surface area of 𝑆. Answer: 𝜋