Question

6.

Which expression represents the volume of the composite figure
formed by a hemisphere with radius r and a cube with side length 2r?

Answer 1

A.
`r^(3)`(
`(2)/(3)`
`\pi` + 8)

Explanation:

A composite figure is formed by two or more shapes in contact.

Volume of a cube =
`l^(3)`

where l is the length of its sides.

Given that l = 2r, then;

volume of the cube =
`(2r)^(3)`

= 8
`r^(3)`

volume of the cube = 8
`r^(3)`

For a hemisphere, volume =
`(2)/(3)`
`\pi`
`r^(3)`

Also,

volume of the hemisphere =
`(2)/(3)`
`\pi`
`r^(3)`

So that,

volume of the composite figure = volume of the cube + volume of the hemisphere

= 8
`r^(3)` +
`(2)/(3)`
`\pi`
`r^(3)`

=
`r^(3)`(8 +
`(2)/(3)`
`\pi`)

volume of the composite figure =
`r^(3)`(
`(2)/(3)`
`\pi` + 8)