 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2021/prelims/mathematics-iv/3/b/i/solution

Interpolate the radius and height by

ρ (t) = a + (c - a) t, z (t) = b + (d - b) t, 0 \leq t \leq 1.

R (t, θ) = (ρ (t) cos θ, ρ (t) sin θ, b + (d - b) t), 0 \leq t \leq 1, 0 \leq θ < 2 π .

The strict positivity of

a, c

gives

ρ (t) > 0

. Since

d > b

, the height identifies

t

uniquely; the angle then identifies a point of each circle uniquely modulo

2 π

. Hence this covers the lateral surface of revolution once. If

a = c

 New to topics? Read the docs here!