Volumes Of Revolution

Question 1

What is the formula for the volume of f(x) when rotated around the x-axis?

Answer 1

π ∫y² dx

Where the limits are interms of x

Question 2

What is the formula for the volume of f(x) when rotated around the y-axis?

Answer 2

π ∫x² dy

Where the limits are in terms of y

Question 3

In volumes of revolution how do you deal with a curve being only partially rotated about the axis?

Answer 3

Work out the volume of the curve if it was rotated through 2π and multiply this by the fraction of the curve that is rotated. e.g if only have the curve is rotated (between 0 and 2π) half your volume

Question 4

What is the formula for the volume of a parametric when rotated around the y-axis?

Answer 4

π ∫x² dy/dt dt

Where the limits have gone from y to t using the y equation

Question 5

What is the formula for the volume of a parametric when rotated around the x-axis?

Answer 5

π ∫y² dx/dt dt

Where the limits have gone from x to t using the x equation

Question 6

If given a diagram thats not got any axis what must you do first before finding the volume of revolution?

Answer 6

Find the origin (the same way you would in polar co-ordinates)