Question
A cone's radius increases x 3 how much will the volume change
Answers
Answered by
GPT 3.5
The volume of a cone is given by the formula V = 1/3 * π * r^2 * h, where r is the radius of the cone and h is the height of the cone.
If the radius of the cone increases by a factor of 3, the new radius will be 3r.
Let's denote the original volume of the cone as V1 and the new volume as V2.
We can calculate the new volume V2 with the new radius 3r:
V2 = 1/3 * π * (3r)^2 * h
V2 = 1/3 * π * 9r^2 * h
V2 = 9/3 * π * r^2 * h
V2 = 3 * V1
Therefore, if the radius of the cone increases by a factor of 3, the volume of the cone will increase by a factor of 3.
If the radius of the cone increases by a factor of 3, the new radius will be 3r.
Let's denote the original volume of the cone as V1 and the new volume as V2.
We can calculate the new volume V2 with the new radius 3r:
V2 = 1/3 * π * (3r)^2 * h
V2 = 1/3 * π * 9r^2 * h
V2 = 9/3 * π * r^2 * h
V2 = 3 * V1
Therefore, if the radius of the cone increases by a factor of 3, the volume of the cone will increase by a factor of 3.