Question

4

10
If the cylinder and the cone shown have the same volume, then the radius
and height of the cone could be which of these?
(2 points)
radius of the cone = 5; height of the cone = 12
radius of the cone = 15; height of the cone = 4
radius of the cone = 15; height of the cone = 12
radius of the cone = 5; height of the cone = 4

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the volume of a cylinder and a cone, we use the following formulas:

Volume of a cylinder = πr^2h
Volume of a cone = 1/3πr^2h

Let's compare the volumes of the cylinder and the cone:

For the cylinder:
Volume = π(10)^2(4) = 400π

For the cone:
Volume = 1/3π(5)^2(12) = 100π

Since the volume of the cylinder is greater than the volume of the cone, the cone with a radius of 5 and a height of 12 is not the correct answer. Let's check the other options:

For the cone with radius 15 and height 4:
Volume = 1/3π(15)^2(4) = 300π

The volume of this cone is also less than the volume of the cylinder, so it is not the correct answer.

For the cone with radius 15 and height 12:
Volume = 1/3π(15)^2(12) = 900π

The volume of this cone is greater than the volume of the cylinder, so this could be a valid solution.

For the cone with radius 5 and height 4:
Volume = 1/3π(5)^2(4) = 100π

This cone has the same volume as the cylinder, so it is also a valid solution.

Therefore, the correct answers are:
- Radius of the cone = 5; Height of the cone = 4
- Radius of the cone = 15; Height of the cone = 12