The diagram shows part of the curve with equation $$\(y=x^{2}+1\)$$. The shaded region enclosed by the curve, the $$\(y\)$$-axis and the line $$\(y=5\)$$ is rotated through $$\(360^{\circ}\)$$ about the $$\(\boldsymbol{y}\)$$-axis. Find the volume obtained. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_m20_qp_12 Year：2020 Question No：3
Answer:
\[
(\pi) \int(y-1) d y
\]
\[
\begin{array}{l}
(\pi)\left[\frac{y^{2}}{2}-y\right]
(\pi)\left[\left(\frac{25}{2}-5\right)-\left(\frac{1}{2}-1\right)\right]
\end{array}
\]
\(8 \pi\) or AWRT \(25.1\)
(\pi) \int(y-1) d y
\]
\[
\begin{array}{l}
(\pi)\left[\frac{y^{2}}{2}-y\right]
(\pi)\left[\left(\frac{25}{2}-5\right)-\left(\frac{1}{2}-1\right)\right]
\end{array}
\]
\(8 \pi\) or AWRT \(25.1\)
Knowledge points:
1.8.4.2 a volume of revolution about one of the axes. (A volume of revolution may involve a region not bounded by the axis of rotation, e.g. the region between and y = 5 rotated about the x-axis.)
Solution:
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