Question

01:34:56

What is the volume of the composite figure? Express the
answer in terms of ..

144mm
168 mm
312 mm
456mm

Answer 1

Third answer choice,
`312\pi` cubic millimeters

Explanation:

The composite figure is attached.

The volume of the figure is the volume of the oblique cone PLUS the volume of half the sphere.

The formula for volume of oblique cone is:

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

The formula for volume of half sphere is:

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

First, volume of oblique cone:

`V=(1)/(3)\pi r^2 h\\V=(1)/(3)\pi (6)^2 (14)\\V=168\pi`

Second, volume of half sphere:

`V=(2\pi r^3)/(3)\\V=(2\pi(6)^3)/(3)\\V=144\pi`

Total Volume of this composite figure is:

`168\pi + 144\pi = 312\pi`