Question

The sum if circumference of four smaller circle of equal radius is equal to the circumference of a bigger circle .find the ratio if area of bigger circle to that of smaller circle​

Answer 1

Answer:

16:1

Step-by-step explanation:

Let the radius of the smaller circles be r and radius of the bigger circle be R

Circumference of 1 small circle = 2πr

∴ Circumference of 4 small circles = 4×2πr = 8πr

Circumference of bigger circle = 2πR

Now, it is given that circumference of four smaller circle is equal to the circumference of a bigger circle

∴ 8πr = 2πR

∴ 4r = R --------eqn 1

Area of bigger circle = πR²

Area of smaller circle = πr²

∴ ratio of area of bigger circle to that of smaller circle​ = πR²/πr²

= R²/r² = (R/r)² = (4r/r)²         [∵R = 4r]

= (4/1)² = 16:1

Answer 2

Step-by-step explanation:

area = circumference

πr^2 = 2πr

r^2 = 2r

r =2