Volumes of revolutionEdexcel A-Level Further Maths: Mind map

Exam questions on Volumes of revolution

1. The region $R$ is bounded by the curve $y=\sqrt x$, the $x$-axis and the line $x=4$.
   The solid formed in (a) is cut so that only the part with $1\leq x\leq4$ remains. Find the exact volume of this part.2 marks
2. The curve $C$ has equation $y=\frac1x$ for $x>0$. All lengths are in centimetres.
   A vase is modelled by rotating the part of $C$ between $x=2$ and $x=5$ through $2\pi$ radians about the $x$-axis. Find the exact volume of the vase.2 marks
3. The finite region $R$ is bounded by the curve $y=x^2$ and the line $y=2x$.
   Find the exact volume generated when $R$ is rotated through $2\pi$ radians about the $x$-axis.3 marks