The radius of base and the volume of a right circular cone are doubled...
Given information
The radius of the base and the volume of a right circular cone are doubled.
Formula for the volume of a cone
The volume (V) of a cone is given by the formula: V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
Effect of doubling the radius on the volume
When the radius of the base is doubled, the new radius becomes 2r.
Using the formula for the volume of a cone, the new volume (V') can be calculated as follows:
V' = (1/3)π(2r)^2h = (1/3)π4r^2h = 4[(1/3)πr^2h] = 4V
This means that when the radius is doubled, the volume of the cone becomes 4 times the original volume.
Effect on the length of the cone
Since the height of the cone is not mentioned in the problem, we cannot directly determine the effect on the length of the cone. However, we can infer that if the radius is doubled while keeping the height the same, the cone would become shorter and wider.
Ratio of the length of larger cone to smaller cone
Since the length of the cone is not directly mentioned in the problem, it is unclear how the length is related to the radius and volume. Therefore, it is not possible to determine the exact ratio of the length of the larger cone to the smaller cone based on the given information.
However, we can conclude that the ratio of the volumes is 4:1 when the radius is doubled. This means that the volume of the larger cone is 4 times the volume of the smaller cone.