Arc length and surface area of revolutionAQA A-Level Further Maths: Mind map

Exam questions on Arc length and surface area of revolution

1. The curve $C$ has equation $y=\frac23x^{3/2}$ for $0\le x\le3$.
   Find the exact length of $C$.2 marks
2. The curve $C$ has equation $y=\sqrt x$ for $0\le x\le2$. It is rotated through $2\pi$ radians about the $x$-axis to form a surface.
   Write down an integral, in terms of $x$, for the area of the surface formed when $C$ is rotated through $2\pi$ about the $y$-axis. Do not evaluate it.2 marks
3. A curve $C$ is given parametrically by $x=3t^2$, $y=2t^3$ for $0\le t\le1$.
   Show that the length of $C$ is given by $\int_0^1 6t\sqrt{1+t^2}\,dt$.3 marks