- 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]{4e1bb995-ce3d-4d16-a0a2-72383489ffe1-04_510_894_443_226}
Find the volume of the funnel according to the model.
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