Question

An expandable cone-shaped funnel consists of two sections as shown.

(a) What is the volume of the bottom section?
(b) What is the volume of the top section?

Answer 1

Explanation:

The bottom section of the funnel is in the shape of cone with radius = 6 cm and height = 8 cm

The volume of a cone is given by
`(1)/(3) \pi r^(2) h\\`

`v=(1)/(3) \pi (3^(2))(8)=24 \pi`

The volume of the top part of the cone, called frustum, is the volume of big cone subtract volume of smaller cone

Volume of big cone =
`(1)/(3)\pi(3^(2))(16)=192\pi`

Volume of frustum =
`192\pi-24\pi=168\pi`

We can leave the answer as an exact answer () or as decimal (527.79 rounded to two decimal places)

Answer 2

The bottom section of the funnel is in the shape of cone with radius = 6 cm and height = 8 cm

The volume of a cone is given by
`(1)/(3) \pi r^(2) h`

`V= (1)/(3) \pi ( 3^(2) )(8)=24\pi`

The volume of the top part of the cone, called frustum, is the volume of big cone subtract volume of smaller cone

Volume of big cone =
`(1)/(3) \pi ( 6^(2) )(16)=192 \pi`

Volume of frustum =
`192 \pi -24 \pi =168 \pi`

We can leave the answer as an exact answer (
`168 \pi`) or as decimal (527.79 rounded to two decimal places)