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A circle is inscribed in a square of side 10cm. Another circle circumscribes the square. What is the ratio of the areas enclosed between the outer circle and square to the are enclosed between the inner circle and square?
- a)(50π − 100)/(100 − 25π)
- b)(100π − 100)/(100 − 50π)
- c)(75π − 100)/(100 − 25π)
- d)(125π − 100)/(100 + 25π)
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A circle is inscribed in a square of side 10cm. Another circle circum...
To solve this problem, let's first find the area of the square and the area of the inner circle.
1. Area of the Square:
The side length of the square is given as 10 cm. Therefore, the area of the square is calculated as:
Area of square = (side length)^2 = 10^2 = 100 cm^2
2. Area of the Inner Circle:
The circle is inscribed in the square, which means the diameter of the circle is equal to the side length of the square. Therefore, the radius of the inner circle is half of the side length of the square.
Radius of the inner circle = (1/2) * side length = (1/2) * 10 = 5 cm
The area of a circle is calculated using the formula:
Area of circle = π * (radius)^2
Substituting the value of the radius in the formula, we get:
Area of inner circle = π * (5)^2 = 25π cm^2
Next, let's find the area of the outer circle.
3. Area of the Outer Circle:
The square is circumscribed by the outer circle, which means the diameter of the outer circle is equal to the diagonal of the square. The diagonal of the square can be found using the Pythagorean theorem.
Diagonal of square = √(side length^2 + side length^2) = √(10^2 + 10^2) = √200 = 10√2 cm
Since the diameter is twice the radius, the radius of the outer circle is equal to half the diagonal of the square.
Radius of outer circle = (1/2) * 10√2 = 5√2 cm
Using the area formula, the area of the outer circle is calculated as:
Area of outer circle = π * (radius)^2 = π * (5√2)^2 = 50π cm^2
Finally, let's find the ratio of the areas enclosed between the outer circle and square to the area enclosed between the inner circle and square.
4. Ratio of the Areas:
Ratio = (Area of outer circle - Area of square) / (Area of square - Area of inner circle)
= (50π - 100) / (100 - 25π)
Therefore, the correct answer is option A) (50π - 100) / (100 - 25π).
1. Area of the Square:
The side length of the square is given as 10 cm. Therefore, the area of the square is calculated as:
Area of square = (side length)^2 = 10^2 = 100 cm^2
2. Area of the Inner Circle:
The circle is inscribed in the square, which means the diameter of the circle is equal to the side length of the square. Therefore, the radius of the inner circle is half of the side length of the square.
Radius of the inner circle = (1/2) * side length = (1/2) * 10 = 5 cm
The area of a circle is calculated using the formula:
Area of circle = π * (radius)^2
Substituting the value of the radius in the formula, we get:
Area of inner circle = π * (5)^2 = 25π cm^2
Next, let's find the area of the outer circle.
3. Area of the Outer Circle:
The square is circumscribed by the outer circle, which means the diameter of the outer circle is equal to the diagonal of the square. The diagonal of the square can be found using the Pythagorean theorem.
Diagonal of square = √(side length^2 + side length^2) = √(10^2 + 10^2) = √200 = 10√2 cm
Since the diameter is twice the radius, the radius of the outer circle is equal to half the diagonal of the square.
Radius of outer circle = (1/2) * 10√2 = 5√2 cm
Using the area formula, the area of the outer circle is calculated as:
Area of outer circle = π * (radius)^2 = π * (5√2)^2 = 50π cm^2
Finally, let's find the ratio of the areas enclosed between the outer circle and square to the area enclosed between the inner circle and square.
4. Ratio of the Areas:
Ratio = (Area of outer circle - Area of square) / (Area of square - Area of inner circle)
= (50π - 100) / (100 - 25π)
Therefore, the correct answer is option A) (50π - 100) / (100 - 25π).
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Community Answer
A circle is inscribed in a square of side 10cm. Another circle circum...
Diameter of inner circle = 10cm.
A1 = 100 - π * 52 = 100 - 25π.
Diameter of outer circle = length of diagonal of square = 10√2.
A2 = π * (5(√2)2 -100 = 50π - 100π.
Option (a) is the correct answer
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A circle is inscribed in a square of side 10cm. Another circle circumscribes the square. What is the ratio of the areas enclosed between the outer circle and square to the are enclosed between the inner circle and square?a)(50π − 100)/(100 − 25π)b)(100π − 100)/(100 − 50π)c)(75π − 100)/(100 − 25π)d)(125π − 100)/(100 + 25π)Correct answer is option 'A'. Can you explain this answer?
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A circle is inscribed in a square of side 10cm. Another circle circumscribes the square. What is the ratio of the areas enclosed between the outer circle and square to the are enclosed between the inner circle and square?a)(50π − 100)/(100 − 25π)b)(100π − 100)/(100 − 50π)c)(75π − 100)/(100 − 25π)d)(125π − 100)/(100 + 25π)Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A circle is inscribed in a square of side 10cm. Another circle circumscribes the square. What is the ratio of the areas enclosed between the outer circle and square to the are enclosed between the inner circle and square?a)(50π − 100)/(100 − 25π)b)(100π − 100)/(100 − 50π)c)(75π − 100)/(100 − 25π)d)(125π − 100)/(100 + 25π)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle is inscribed in a square of side 10cm. Another circle circumscribes the square. What is the ratio of the areas enclosed between the outer circle and square to the are enclosed between the inner circle and square?a)(50π − 100)/(100 − 25π)b)(100π − 100)/(100 − 50π)c)(75π − 100)/(100 − 25π)d)(125π − 100)/(100 + 25π)Correct answer is option 'A'. Can you explain this answer?.
A circle is inscribed in a square of side 10cm. Another circle circumscribes the square. What is the ratio of the areas enclosed between the outer circle and square to the are enclosed between the inner circle and square?a)(50π − 100)/(100 − 25π)b)(100π − 100)/(100 − 50π)c)(75π − 100)/(100 − 25π)d)(125π − 100)/(100 + 25π)Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A circle is inscribed in a square of side 10cm. Another circle circumscribes the square. What is the ratio of the areas enclosed between the outer circle and square to the are enclosed between the inner circle and square?a)(50π − 100)/(100 − 25π)b)(100π − 100)/(100 − 50π)c)(75π − 100)/(100 − 25π)d)(125π − 100)/(100 + 25π)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle is inscribed in a square of side 10cm. Another circle circumscribes the square. What is the ratio of the areas enclosed between the outer circle and square to the are enclosed between the inner circle and square?a)(50π − 100)/(100 − 25π)b)(100π − 100)/(100 − 50π)c)(75π − 100)/(100 − 25π)d)(125π − 100)/(100 + 25π)Correct answer is option 'A'. Can you explain this answer?.
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