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
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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
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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