Question

The sum of circumferences of four small circles of equal radius is equal to the
circumference of a bigger circle. Find the ratio of the area of the bigger circle to that o
the smaller circle.
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Answer 1

Answer:

16 : 1

Step-by-step explanation:

Let the radius of small circles be r and that of big circle be R.

Circumference of each small circle = 2πr, since small circles have same radius their circumference is equal.

Circumference of big circle = 2πR.

Here, sum of circumferences of four small circles of equal radius is equal to the

circumference of a bigger circle, which means,

=> 2πr + 2πr + 2πr + 2πr = 2πR

=> 8πr = 2πR

=> 4r = R

Ratio of area of bigger to smaller circle:

=> area(big) ; area(small)

=> (πR²) / (πr²)

=> R² / r² , note that 4r = R

=> (4r)² / r²

=> 16r²/r²

=> 16

Answer 2

Answer:

circumference =3 area

2πr = 3π r^2

2r = 3r^2

2= 3r

3/2= r