Question

Given two circles whose radii are 35" and 28", the ratio of their areas is
10 to 16
5 to 4
25 to 16
25 to 8

Thanks for the help, will fan & medal!

Answer 1

You could do it the "hard way"
Area of a circle is
\[ A = \pi r^2 \]
so the ratio of areas is
\[ \frac{\pi \cdot 35\cdot 35}{\pi \cdot 28\cdot 28} \]
which you can simplify

but in general, similar shapes with *sides* in the ratio of " a : b" will have their areas in the ratio of a^2 : b^2

Answer 2

so simplify I would write 35 as 5*7 and 28 as 4*7 , so the ratio of areas is
\[ \frac{ \pi \cdot 5 \cdot 7 \cdot 5 \cdot 7 }{\pi \cdot 4 \cdot 7 \cdot 4 \cdot 7 }\]

now cancel things that are in both the top and bottom
\[ \frac{ \cancel{\pi} \cdot 5 \cdot \cancel{7} \cdot 5 \cdot \cancel{7} }{\cancel{\pi} \cdot 4 \cdot \cancel{7} \cdot 4 \cdot \cancel{7} }\]