To determine the correct answer, we first need to calculate the volume of the cylinder.
Volume of cylinder = πr^2h
Volume of cylinder = π(5^2)(4)
Volume of cylinder = π(25)(4)
Volume of cylinder = 100Ï€
Since the volume of the cylinder is 100Ï€, the volume of the cone must also be 100Ï€ in order for them to have the same volume.
The formula for the volume of a cone is V = 1/3Ï€r^2h, where r is the radius and h is the height.
100Ï€ = 1/3Ï€r^2h
100 = 1/3 r^2h
300 = r^2h
Now, let's examine the answer choices:
1. radius = 5; height = 4
r = 5, h = 4
5^2 * 4 = 100, so this is a possible solution
2. radius = 15; height = 12
r = 15, h = 12
15^2 * 12 = 2700, this does not equal 300, so this is not a possible solution
3. radius = 15; height = 4
r = 15, h = 4
15^2 * 4 = 900, this does not equal 300, so this is not a possible solution
4. radius = 5; height = 12
r = 5, h = 12
5^2 * 12 = 300, this equals 300, so this is a possible solution
Therefore, the correct choices are:
radius of the cone = 5; height of the cone = 4
and
radius of the cone = 5; height of the cone = 12