Question

Two cones have a radius of 2 cm. The height of one cone is 8 cm. The other cone is 1/4 of that height. Which of these statements is NOT true?

Answer 1

Out of given option only option (d) is wrong.

The volume of the smaller cone cannot be determined because its height is unknown.

Explanation:

Given two cones with radius 2 cm.

The height of one cone is 8 cm an the height of other cone is
`(1)/(4)` of the height of first cone.

Height of second cone =
`(1)/(4)` of the height of first cone.

=
`(1)/(4)* 8=2`

Volume of cone =
`(1)/(3) \pi r^2h`

Thus, Volume of smaller cone =
`(1)/(3) \pi (2)^2 \cdot(1)/(4)* 8`

=
`(1)/(3) \pi (2)^2 \cdot 2`

=
`(1)/(3) 4 \pi\cdot 2`

Thus, out of given option only option (d) is wrong.

The volume of the smaller cone cannot be determined because its height is unknown.

Answer 2

The wrong statement: The volume or the smaller cone cannot be determined because its height is unknown.

We already know that the larger cone has a height of 8 cm and that the smaller cone is just 1/4 of 8 cm.

8×1/4 = 2 cm.

You can still find its volume by using the formula 1/3πr^2.