Question

The sum of circumferences of four small circles is equal to the circumference of bigger circle.find the ratio of the area of the bigger circle to that of the smaller circle? by full process

Answer 1

Hi friend!

Answer:

Right now, radius is unknown.
Let's take radius as r.

Sum of circumferences of four small congruent circles = 4 × 2πr = 8πr

It is equal to circumference of the larger circle.
So the radius of the larger circle would be:

If 2πR = 8πr
$\pi R = \frac{8\pi r}{2} = 4\pi r \\ \\ R = \frac{4πr}{π} \\ R = 4r$
So radius of bigger circle = 4r

Area of smaller circle = πr²

Area of larger circle = πR² = π(4r)²
= 16πr²

Ratio = πr² : 16πr²
$= \sout{\pi r^2} \: : \: 16\sout{\pi r^2} \\ = 1 \: : \: 16$

Hope you found my answer helpful. Keep Smiling!

Answer 2

Answer:

Hope it can help you

Step-by-step explanation: