 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-2/19/c/solution

The ratio of the two maximal volumes is

\frac{V _{c, m a x}}{V _{p, m a x}} = \frac{π}{2} > 1 .

Thus the cylinder has the larger maximum volume, by a factor

π /2

. Both optimal shapes have height

H /2

, while their horizontal cross-sections have areas

π R^{2} /2

and

R^{2}

, respectively.

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