Question

two circles are similar. If the larger circle has an area that is 225 times larger than the small circle, how many times bigger is its radius?

Answer 1

SOLUTION:

Case: Areas

Metho:

The larger circle has an area that is 225 times larger than the small circle.

Let the large area be 'A' and the radius is R

AND thesmaller area be a'' and radius is Rr

$\frac{A}{a}=225$

Applying the formula for Area of the similar circles

$\begin{gathered} \frac{A}{a}=225 \\ \frac{\pi R^2}{\pi r^2}=225 \\ \frac{R^2}{r^2}=225 \\ Take\text{ }the\text{ }square-root\text{ } \\ \sqrt{\frac{R^2}{r^2}}=\sqrt{225} \\ \frac{R}{r}=15 \\ R=15r \end{gathered}$

Final answers:

From the above, the bigger circle has a rdius i5 times tehe smaller one