3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{09bd14c0-c368-4ae1-bee0-cc8bf82abecc-06_582_588_255_758}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a circle with radius \(r\) and centre at the origin.
The region \(R\), shown shaded in Figure 1, is bounded by the \(x\)-axis and the part of the circle for which \(y > 0\)
The region \(R\) is rotated through \(360 ^ { \circ }\) about the \(x\)-axis to create a sphere with volume \(V\)
Use integration to show that \(V = \frac { 4 } { 3 } \pi r ^ { 3 }\)