Volumes of revolutionEdexcel International A Level Maths: Flashcards

What these 12 flashcards ask

Formula for volume of revolution about the x-axis?
Where does the \pi y^2\,\delta x come from?
Is \pi\int x^2\,dy required?
What is (2\sqrt{x})^2?
What is (e^{2x})^2?
Volume when y=2\sqrt x, from x=1 to 4?
Formula for volume with parametric equations x=f(t), y=g(t)?
What must you do with the limits in a parametric integral?
How do you find the limits when a curve meets the x-axis?
Integral of \frac{1}{2x+1}?
Common error with (a+b)^2 inside the integrand?
Why leave \pi outside the integral?

Exam questions on Volumes of revolution

The region $R$ is bounded by the curve $y=2\sqrt{x}$ , the $x$ -axis and the lines $x=1$ and $x=4$ . The region $R$ is rotated through $2\pi$ radians about the $x$ -axis to form a solid.
The line $x=4$ is replaced by the line $x=a$ , where $a>1$ . The volume of the new solid is $48\pi$ . Find the value of $a$ .2 marks
The region $S$ is bounded by the curve $y=e^{2x}$ , the coordinate axes and the line $x=1$ . The region $S$ is rotated through $2\pi$ radians about the $x$ -axis to form a solid.
The line $x=1$ is replaced by the line $x=\ln2$ . Find the exact volume of the new solid.2 marks
The region $R$ is bounded by the curve $y=\frac{1}{\sqrt{2x+1}}$ , the coordinate axes and the line $x=4$ . The region $R$ is rotated through $2\pi$ radians about the $x$ -axis to form a solid.
Show that the volume of the solid is $\pi\ln3$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).