5.12 Areas and volumes of revolutionIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 5.12 Areas and volumes of revolution

1. The curve $C$ has equation $y=x^2-4x$.
   Use your GDC to find the total area enclosed between $C$ and the $x$-axis for $0\le x\le6$.2 marks
2. For $k>0$, the region $R_k$ is enclosed by the curve $y=\sqrt{x}$, the $x$-axis and the line $x=k$. The region is rotated through $360^\circ$ about the $x$-axis to form a solid of volume $V$.
   Find the value of $k$ for which $V=18\pi$.2 marks
3. The curve $y=x^2$ is drawn for $x\ge0$. Distances are in centimetres. The region $S$ is enclosed by the curve, the $y$-axis and the line $y=9$.
   The region $S$ is rotated through $360^\circ$ about the $y$-axis to model a bowl. Find the exact volume of the bowl.3 marks