1 answer
(click or scroll down)
The volume of a sphere is given by the formula V = (4/3)Ï€r^3, where r is the radius of the sphere.
If the radius of the sphere increases by a factor of x, then the new radius would be x times the original radius.
Let's say the original radius is r, then the new radius would be x*r.
The new volume of the sphere would be V_new = (4/3)Ï€(xr)^3 = (4/3)Ï€x^3r^3.
To find out how many times the volume has increased, we can divide the new volume by the original volume:
V_new/V = (4/3)Ï€x^3r^3 / (4/3)Ï€r^3 = x^3.
Therefore, if the radius of a sphere increases by a factor of x, its volume will increase by a factor of x^3.