Question

The volume of solid of revolution when rotated along y-axis is given as ________

(a) \(\int_a^b πy^2 dx \)

(b) \(\int_a^b πy^2 dy \)

(c) \(\int_a^b πx^2 dx \)

(d) \(\int_a^b πx^2 dy \)

The question was asked in an online quiz.

My enquiry is from Volume of Solid of Revolution topic in chapter Integral Calculus of Engineering Mathematics

Answer 1

Right option is (d) \(\int_a^b πx^2 dy \)

To explain: Volume is generated when a 2d surface is revolved along its axis. When revolved along y-axis, the volume is given as \(\int_a^b πx^2 dy \).