The surface area of a sphere is

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

and

the first r is 2.68 and the second r is 8.03
then,

or rounded off to 3.
Make the denominators equal by multiplying them:

Subtract:

Simplify:

The answer is

or 0.16
Diameter=14cm
Radius=14 divided by 2
Radius=7cm
I'm not completely sure about what you are asking, but if its what i'm taking from this, tan A = 7/9 is finding the measure of angle A.