f the perimeter of a circle is equal to that of a square, then the ratio of their areas is 22: 7 14: 11 7: 22 11: 14
Question
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is:
- 22: 7
- 14: 11
- 7: 22
- 11: 14
Solution
The perimeter of a circle is given by 2πr, and the perimeter of a square is given by 4s, where r is the radius of the circle and s is the side length of the square.
If the perimeters are equal, then we have 2πr = 4s. Solving for s, we get s = πr/2.
The area of a circle is given by πr², and the area of a square is given by s². Substituting s = πr/2 into the area of the square, we get the area of the square is (πr/2)² = π²r²/4.
The ratio of the area of the circle to the area of the square is then (πr²) / (π²r²/4) = 4/π.
Therefore, the ratio of their areas is 4/π : 1, which is approximately 1.27 : 1. This is not one of the options given in the question. There may be a mistake in the question or the provided options.
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