- The region \(R\) is bounded by the curve \(x = \sin y\), the \(y\)-axis and the lines \(y = 1 , y = 3\). Find the volume of the solid generated when \(R\) is rotated through four right angles about the \(y\)-axis. Give your answer correct to two decimal places.
- (a) Determine the number of solutions of the equations
$$\begin{array} { r }
x + 2 y = 3
2 x - 5 y + 3 z = 8
6 y - 2 z = 0
\end{array}$$
(b) Give a geometric interpretation of your answer in part (a).