Find the normal to the surface Let A be the area of the hemisphere of radius 8 w

Question

Find the normal to the surface

Let A be the area of the hemisphere of radius 8 which given by: x2 + y2 + z2 = 64 where 0 z 4 Indicate the correct parameterisation of the surface: (.x, y, z) = S(u, v) = 64(cos u sin v, sin u sin v, cos v); where 0 u 2 pi, pi /3 v pi /2 (x, y, z) = S(u, v) = 8(cos u sin v, sin u sin v, cos v); where 0 u 2 pi, pi /3 v pi /2 (x, y, z) = S(u, v) = 8(cos u sin v, sin u sin v, cos v); where 0 u 2 pi, 0 v (x, y, z) = S(u, v) = 8(cos u sin v, sin u sin v, cos v); where 0 v 2 pi, pi /3 u pi /2. Find the normal to the surface N(u, v) = Times = Answer is a Vector Evaluate the area A = Answer is a Number

Explanation / Answer

1) (b)

2) -64[ (cosu)(sinv)^2 i + (sinv)^2 (sinu) j +sinv cosv k]

3) 64* pi

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