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\includegraphics[max width=\textwidth, alt={}, center]{b2cefbd6-6e89-495a-9f42-60f76c8c5975-4_556_524_255_813}
The diagram shows the circular cross-section of a uniform cylindrical log with centre \(O\) and radius 20 cm . The points \(A , X\) and \(B\) lie on the circumference of the cross-section and \(A B = 32 \mathrm {~cm}\).
- Show that angle \(A O B = 1.855\) radians, correct to 3 decimal places.
- Find the area of the sector \(A X B O\).
The section \(A X B C D\), where \(A B C D\) is a rectangle with \(A D = 18 \mathrm {~cm}\), is removed.
- Find the area of the new cross-section (shown shaded in the diagram).