10
\includegraphics[max width=\textwidth, alt={}, center]{56d376c5-b91f-488d-89e2-18edcb14052d-4_799_1390_255_376}
The diagram shows the curve \(y = \sqrt { } ( 1 + 2 x )\) meeting the \(x\)-axis at \(A\) and the \(y\)-axis at \(B\). The \(y\)-coordinate of the point \(C\) on the curve is 3 .
- Find the coordinates of \(B\) and \(C\).
- Find the equation of the normal to the curve at \(C\).
- Find the volume obtained when the shaded region is rotated through \(360 ^ { \circ }\) about the \(\boldsymbol { y }\)-axis.