 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/16/b/i/solution

Parameterize the surface by

r (x, z) = (x, 1 + z, z)^{T}

(1, 0, 0)^{T}

and

(0, 1, 1)^{T}

(0, - 1, 1)^{T}

2

d S = 2 d x d z .

Equivalently, projection onto the

x z

-plane reduces the surface area by

∣ n \cdot e_{y} ∣ = 1/ 2

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