To solve this problem, we need to use the formula for the volume of a cylinder and a cone.
The volume of a cylinder is calculated as V_cylinder = πr^2h, where r is the radius of the cylinder, and h is the height of the cylinder.
The volume of a cone is calculated as V_cone = 1/3πr^2h, where r is the radius of the cone, and h is the height of the cone.
Given that the volume of the cylinder and the cone are the same, we can equate the two formulas:
πr^2(4) = 1/3πr^2h
First, simplify the equation by canceling out the common factors:
4 = 1/3h
Thus, 12 = h.
Since the height of the cone is 12, the only possible answer is option B: Radius of the cone = 15; height of the cone = 12.
an image shows a cylinder with a height of 4 and width of 10, and a cone with no confirmed height or diameter.
If the cylinder and the cone in the image had the same volume, then the radius and height of the cone could be which of these?
A: Radius of the cone = 15; height of the cone = 4
B: Radius of the cone = 15; height of the cone = 12
C: Radius of the cone = 5; height of the cone = 4
D: Radius of the cone = 5; height of the cone = 12
1 answer