Question

Segment AB is completely rotated about the y-axis to form a 3-D figure. Find the volume of the figure. The

length of AB is 6.

Answer 1

The volume of the figure is 905 cubic units.

Explanation:

Rotation is a method of solid transformation which involve turning a given line, or object about a reference point. In the given question, rotating segment AB completely about the y-axis would form a 3 dimensional figure of a sphere.

volume of a sphere =
`(4)/(3)`
`\pi`
`r^(3)`

where r is the radius of the sphere.

Given that AB = 6, then the radius of the sphere = 6

volume of sphere =
`(4)/(3)` x
`(22)/(7)` x
`(6)^(3)`

=
`(88)/(21)` x 216

= 905.14

volume of sphere = 905 cubic units

The volume of the figure is 905 cubic units.