Question

the ratio of the radii of two spheres is 6 : 5, what is the ratio of the surface areas of the two spheres?

Answer 1

\[\large r_1:r_2 \qquad\rightarrow\qquad 6:5\]

Surface Area of a Sphere is given by, \(\large 4\pi r^2\)

So the ratio of their surface areas will be,

\[\large 4\pi (r_1)^2:4\pi (r_2)^2 \qquad\rightarrow\qquad 4\pi(36):4\pi(25)\]
And from there, we sould probably simplify the ratio by dividing both terms by 4pi.
Yah I think we can do that...

Any confusion? :o

Answer 2

or you can use the idea that if the ratio of two sides is a/b, then the ratio of two areas is (a/b)^2 = (a^2)/(b^2)