A right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is:3 : 52 : 53 : 11 : 3
Question
A right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is:3 : 52 : 53 : 11 : 3
Solution
To find the ratio of the height of the cylinder to that of the cone, we can use the formula for the volume of a cylinder and a cone.
The volume of a cylinder is given by V_cylinder = πr^2h_cylinder, where r is the radius and h_cylinder is the height of the cylinder.
The volume of a cone is given by V_cone = (1/3)πr^2h_cone, where r is the radius and h_cone is the height of the cone.
Given that the radius of the cylinder and the cone are the same, we can set the volumes equal to each other:
πr^2h_cylinder = (1/3)πr^2h_cone
Canceling out the common factors, we get:
h_cylinder = (1/3)h_cone
Therefore, the ratio of the height of the cylinder to that of the cone is 1:3.
So, the correct answer is 1:3.
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