If a spherical ball is enlarged so that its surface area is 9 times greater than its original surface area, then the original radius was multiplied by___?
To find the change in radius when the surface area is multiplied by a certain factor, we need to understand the relationship between surface area and the radius for a sphere.
The surface area of a sphere is given by the formula A = 4πr^2, where A represents the surface area and r represents the radius.
In this case, we are given that the new surface area is 9 times greater than the original surface area. Let's represent the original surface area as A1 and the new surface area as A2.
We can set up the equation:
A2 = 9 * A1
By substituting the surface area formula, we get:
4πr2 = 9 * 4πr1^2
Dividing both sides of the equation by 4π, we have:
r2^2 = 9 * r1^2
Taking the square root of both sides, we get:
r2 = 3 * r1
Thus, the new radius is 3 times greater than the original radius.
To answer your question specifically, the original radius was multiplied by 3.
area grows by a factor of n^2 means radius grows by n.
9 = 3^2
so . . .