# Exam-Style Question on Volume of Revolution

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 720. This question is similar to one that appeared on an IB AA Higher paper in 2023. The use of a calculator is not allowed.

The function $$f$$ is defined by $$f(y) = \sqrt{y^2 + 10y}$$ for $$0 \leq y \leq 8$$.

The region enclosed by the graph of $$x = f(y)$$ and the $$y$$-axis is rotated by $$360^\circ$$ about the $$y$$-axis to form a solid weight. The weight is drilled through from the top along the $$y$$-axis, creating a cylindrical hole 6 units deep. The volume of the remaining weight is 1000 cubic units.

Find the radius of the cylindrical hole that was drilled through the weight.

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