 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-2/8/solution

y^{2} + x^{2} + z^{2} = r^{2}

4 π

and the volume element contributes

r^{2} d r

. Thus

∭_{r \leq R} \nabla \cdot F d V = 4 π \int_{0}^{R} r^{4} d r = \frac{4 π R ^{5}}{5} .

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