Volumes of Revolution

Question 1

Volume when rotated 360 about the x-axis

Answer 1

a
V = π ∫ y^2 dx
b
Definitely integrate the square of the function and multiply by pi

Question 2

When it is rotated about the x-axis by not 360

Answer 2

Solve as if it was 360

Multiply by angle/360

Question 3

Volume when rotated 360 about the y-axis

Answer 3

a
V = π ∫ x^2 dy
b
You need to rearrange in terms of x

Question 4

Area of a cone

Answer 4

V = 1/3 π r^2h

Question 5

If you have a triangle

Answer 5

It will form a cone when revolved around the axis

Question 6

If you have a rectangle

Answer 6

It will form a cylinder when revolved around the axis

Question 7

What do you do if your shape is symmetrical around the y-axis and you rotate it around the y

Answer 7

You should only use the shape on one side of the axis, do both sides still on x

Question 8

How to deal with volumes between a curve and a line

Answer 8

You can’t subtract the equations so find each volume separately