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Q 1. Let S = G(D), where D = { (u, v): u2 + v2 ? 64, u ? 0, v ? 0 } and G(u, v) = (2u + 1, u ? v, 3u + v).

Calculate the surface area of S.

Q 2. Calculate f(x, y, z) dS for the given surface and function.

G(r, ?) = (r cos ?, r sin ?, ?), 0 ? r ? 5, 0 ? ? ? 2?; f(x, y, z) =

Q 3. Calculate f(x, y, z) dS for the given surface and function.

y = 9 ? z2, 0 ? x ? 3, 0 ? z ? 3; f(x, y, z) = z

Q 4. Calculate f(x, y, z) dS for the given surface and function.

x2 + y2 + z2 = 1, x, y, z ? 0; f(x, y, z) = 5x2.

Q 5. Calculate f(x, y, z) dS for the given surface and function.

x2 + y2 = 36, 0 ? z ? 4; f(x, y, z) = e?z

Q 6. Calculate f(x, y, z) dS for the given surface and function.

G(u, v) = (u, v3, u + v), 0 ? u ? 1, 0 ? v ? 1; f(x, y, z) = 9y.

Q 7. Calculate f(x, y, z) dS for the given surface and function.

Part of the plane x + y + z = 0 contained in the cylinder

x2 + y2 = 1; f(x, y, z) = 7z2

Q 8. Calculate f(x, y, z) dS for f(x, y, z) = e?z, where x2 + y2 = 4 and 0 ? z ? 6.

Q 9. Calculate f(x, y, z)dS for the given surface and function.

x2 + y2 + z2 = 16, 0 ? y ? 1; f(x, y, z) = y

Q 10. Find the surface area of the part of the cone x2 + y2 = z2 between the planes z = 3 and z = 7

Q 11. Find the surface area of the portion S of the cone z2 = x2 + y2, where z ? 0, contained within the cylinder y2 + z2 ? 36.

Q12. Use cylindrical coordinates to compute the surface area of a sphere of radius R = 9

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