if a cones radius increases x 3 how many x will its volume increase
The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
If the radius of the cone increases by a factor of 3, then the new radius will be 3r.
Let's consider the volume of the cone with the original radius and the volume of the cone with the new radius:
V_original = (1/3) * π * r^2 * h
V_new = (1/3) * π * (3r)^2 * h = (1/3) * π * 9r^2 * h = 3 * (1/3) * π * r^2 * h = 3 V_original
Therefore, the volume of the cone will increase by a factor of 3.