 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-1/5/b/solution

The two radii enclose the angle

2 π /3

, so the triangle has area

T = \frac{1}{2} r^{2} sin (2 π /3) = 3 r^{2} /4

. From the sector calculation,

r^{2} = 3 B / π

. Consequently

T = \frac{3 3}{4 π} B .

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