5 Use de Moivre's theorem to find the constants \(A , B\) and \(C\) in the identity \(\sin ^ { 5 } \theta \equiv A \sin \theta + B \sin 3 \theta + C \sin 5 \theta\).
\(6 O\) is the origin of a coordinate system whose units are cm .
The points \(A , B , C\) and \(D\) have coordinates ( 1,0 ), ( 1,4 ), ( 6,9 ) and ( 0,9 ) respectively.
The arc \(B C\) is part of the curve with equation \(x ^ { 2 } + ( y - 10 ) ^ { 2 } = 37\).
The closed shape \(O A B C D\) is formed, in turn, from the line segments \(O A\) and \(A B\), the arc \(B C\) and the line segments \(C D\) and \(D O\) (see diagram).
A funnel can be modelled by rotating \(O A B C D\) by \(2 \pi\) radians about the \(y\)-axis.
\includegraphics[max width=\textwidth, alt={}, center]{58e9b480-f561-4a28-b911-7d9d6a80e976-3_641_1131_808_242} Find the volume of the funnel according to the model.