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 _________.
The surface area of a sphere is [tex]A = 4 \pi r^{2} [/tex] and if the original S.A was is enlarged to have it 9 times greater, the radius would be multiplied by 3 or roughly 2.99626 rounded off to 3.0.
For example, let us assign values. Let A=90
A= 90*9 = 810
[tex]90 = 4 \pi r^{2}
[/tex] and [tex]810 = 4 \pi r ^{2} [/tex]
the first r is 2.68 and the second r is 8.03
then, [tex] \frac{8.03}{2.68} = 2.99626 [/tex] or rounded off to 3.
