The document discusses calculating the volume of solids of revolution using integrals. It provides the formula for finding the volume of a solid rotated about the x-axis between x=a and x=b using a cross-sectional area function A(x). It then works through an example of finding the volume of a right circular cone of height 4 and base radius 1, and confirms the result matches the standard volume formula for a cone.

1. Volume by slices

2. y
x
a b

3. The volume of a solid between x = a and x = b
having a cross­sectional are A(x) at input x is:
b
V = A(x) dx
a

4. Find the volume of a right circular cone with base
radius 1 and height 4.
4
V = A(x) dx
0
0 x 4
2
x
A(x) =
16

6. V = 1 r2 h
3
= 1 (1)2 4
3
= 4
3
Confirms value from previous screen

7. If the function below is revolved about the x­axis, find the volume
of the solid generated between f, the x­axis, x = 0, and x = 2.
f(x) = x2

9. Exercise 8.2
Questions 1 ­ 9