CAPE Pure Mathematics Unit 1 · May/June 2010 · Paper 1 · Question Q35

Item 35 refers to the diagram below. The finite region R is enclosed by the curve y = x^2, the y-axis and the line y = 3 as shown in the diagram above. This region is rotated completely about the y-axis to form a soild of revolution. The volume of this solid is given by

1. (A)\pi \int_0^3 x^4\,\mathrm{d}x
2. (B)\pi \int_0^{\sqrt{3}} x^4\,\mathrm{d}x
3. (C)\pi \int_0^3 y^2\,\mathrm{d}y
4. (D)\pi \int_0^3 y\,\mathrm{d}y

This question uses a figure or table from the paper — you'll see it when you practise.