## Exam-Style Question on Volume of Revolution## A mathematics exam-style question with a worked solution that can be revealed gradually |

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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