To find the volume of a cylinder, we use the formula V_cylinder = πr^2h, where r is the radius and h is the height. To find the volume of a cone, we use the formula V_cone = (1/3)πr^2h.
Given that the first cylinder has a height of 4 and a radius of 10, the volume of the cylinder is V_cylinder = π(10^2)(4) = 400π.
Since the cylinder and cone have the same volume, the volume of the cone is also 400π. Using the second set of dimensions, we can calculate the volume of the cone: V_cone = (1/3)π(5^2)(12) = 100π. This volume does not match the volume of the cylinder, so the first option is incorrect.
Using the third set of dimensions, we calculate the cone volume: V_cone = (1/3)π(5^2)(4) = 100π. This volume does match the cylinder volume, so the radius of the cone = 5 and the height of the cone = 4 is correct.
The fourth set of dimensions also does not match the cylinder volume, so it is incorrect.
Therefore, the radius of the cone = 5 and the height of the cone = 4 are the correct dimensions for the cone to have the same volume as the given cylinder.
1. height: 4 Radius: 10
2. height: ? radius:?
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 =5: height of the cone= 4
radius of the cone= 15 : height of the cone= 12
1 answer
1 answer