# How do you find the volume bounded by #x-8y=0# & the lines #x+2y# revolved about the y-axis?

##### 1 Answer

Volume of revolution =

#### Explanation:

The ihtersection of the two lines happen to be,

^3Considering y axis to represent the height of the cone,

Area of cross section is given by

where,

r is the x coordinate.

For x-8y=0, from y=0 to y=a/10,

x=8y

A=pi(x)^2

A=pi(8y)^2

Volume1 =

For x=2y=1 from y=a/10 to y=a/2

A=pi(x)^2

Volume2=

Volume2=

Volume of revolution = Volume1+Volume2

Volume of revolution =