Volume of revolution formula (H2 maths)

• Mad Hat

  29 Jul 13, 18:25

  If the area below a curve y=f(x) from x=a to x=b is rotated 360 degrees about the x-axis, then the volume of revolution is given by:

  π ∫ y² dx , with limits a and b.

  

  But if the same area is rotated 360 degrees around the y-axis instead, then C.S. Toh (A-level study guide) gives this formula for the volume of revolution:

  2π ∫ xy dx , with limits a and b.

  Is this second formula in the H2 maths syllabus also? Are A-level students expected to know it? (Obviously, the first formula must be known. But this second one, I'm not so sure.)

• Seowlah

  29 Jul 13, 23:37

  The second formula is NOT required in the H2 syllabus as the students can use the formula π ∫ x² dy and the big volume minus the small volume to get the shaded volume.

  However, the formula can come in handy as a short cut method.

• Mad Hat

  30 Jul 13, 15:46

  Thanks!