Question

A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis. What is the volume of the figure?

Answer 1

Given:

A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis.

To find:

The volume of the figure.

Solution:

Points A(0,0) and C(0,9) lies on the y-axis. Length of AC is 9 units.

Points A(0,0) and B(6,0) lies on the x-axis. Length of AB is 6 units.

If a triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis, then it will form a cone with radius 6 units and height 9 units.

Volume of a cone is

`V=(1)/(3)\pi r^2h`

where, r is radius of the base and h is vertical height of the cone.

Putting r=6 and h=9, we get

`V=(1)/(3)\pi (6)^2(9)`

`V=\pi (36)(3)`

`V=108\pi`

Therefore, the volume of the figure is
`108\pi` sq. units.