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Circumference of a circle-A is 5/4 times perimeter of a square. Area of the square is 961 sq. cm. What is the area of another circle-B whose diameter is half the radius of the circle-A?
- a)167.3 sq cm
- b)125.8 sq cm
- c)118.9 sq cm
- d)181.2 sq cm
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Circumference of a circle-A is 5/4 times perimeter of a square. Area o...
The side of the square = a=√961=31 cm.
Perimeter = 4 X 31 = 124 cm The circumference of the circle = 5/4 x 124 = 22/7 x 2 x r
Radius = 155*7/44 = 24.6 cm
Half the radius of Circle-A = 12.3 cm.
Radius of Circle-B = 14/2 = 6.15 cm
The area = 22/7 x 6.15 x 6.15 = 54 cm2
Perimeter = 4 X 31 = 124 cm The circumference of the circle = 5/4 x 124 = 22/7 x 2 x r
Radius = 155*7/44 = 24.6 cm
Half the radius of Circle-A = 12.3 cm.
Radius of Circle-B = 14/2 = 6.15 cm
The area = 22/7 x 6.15 x 6.15 = 54 cm2
Most Upvoted Answer
Circumference of a circle-A is 5/4 times perimeter of a square. Area o...
To solve this question, we need to follow these steps:
1. Find the circumference of circle A
2. Find the perimeter of the square
3. Find the radius of circle A
4. Find the diameter of circle B
5. Find the radius of circle B
6. Find the area of circle B
1. Find the circumference of circle A:
Given that the circumference of circle A is 5/4 times the perimeter of the square, we can write the equation as:
Circumference of circle A = 5/4 * Perimeter of square
2. Find the perimeter of the square:
The area of the square is given as 961 sq. cm. The formula to find the area of a square is side^2, where side is the length of one side of the square. So, we can write the equation as:
side^2 = 961
Taking the square root on both sides, we get:
side = √961 = 31 cm
The perimeter of a square is given by the formula 4 * side, so the perimeter of the square is:
Perimeter of square = 4 * 31 = 124 cm
3. Find the radius of circle A:
We know that the circumference of a circle is given by the formula 2 * π * radius. So, we can write the equation as:
2 * π * radius A = 5/4 * 124
Simplifying the equation, we get:
radius A = (5/8) * 124 * (1/π) = 77.5 cm
4. Find the diameter of circle B:
The diameter of circle B is half the radius of circle A, so:
Diameter of circle B = 2 * (radius A / 2) = radius A = 77.5 cm
5. Find the radius of circle B:
The radius of circle B is half the diameter, so:
Radius of circle B = (1/2) * 77.5 = 38.75 cm
6. Find the area of circle B:
The area of a circle is given by the formula π * radius^2. So, we can calculate the area of circle B as:
Area of circle B = π * (38.75)^2 ≈ 118.9 sq cm
Therefore, the area of circle B is approximately 118.9 sq cm, which corresponds to option (c).
1. Find the circumference of circle A
2. Find the perimeter of the square
3. Find the radius of circle A
4. Find the diameter of circle B
5. Find the radius of circle B
6. Find the area of circle B
1. Find the circumference of circle A:
Given that the circumference of circle A is 5/4 times the perimeter of the square, we can write the equation as:
Circumference of circle A = 5/4 * Perimeter of square
2. Find the perimeter of the square:
The area of the square is given as 961 sq. cm. The formula to find the area of a square is side^2, where side is the length of one side of the square. So, we can write the equation as:
side^2 = 961
Taking the square root on both sides, we get:
side = √961 = 31 cm
The perimeter of a square is given by the formula 4 * side, so the perimeter of the square is:
Perimeter of square = 4 * 31 = 124 cm
3. Find the radius of circle A:
We know that the circumference of a circle is given by the formula 2 * π * radius. So, we can write the equation as:
2 * π * radius A = 5/4 * 124
Simplifying the equation, we get:
radius A = (5/8) * 124 * (1/π) = 77.5 cm
4. Find the diameter of circle B:
The diameter of circle B is half the radius of circle A, so:
Diameter of circle B = 2 * (radius A / 2) = radius A = 77.5 cm
5. Find the radius of circle B:
The radius of circle B is half the diameter, so:
Radius of circle B = (1/2) * 77.5 = 38.75 cm
6. Find the area of circle B:
The area of a circle is given by the formula π * radius^2. So, we can calculate the area of circle B as:
Area of circle B = π * (38.75)^2 ≈ 118.9 sq cm
Therefore, the area of circle B is approximately 118.9 sq cm, which corresponds to option (c).
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Circumference of a circle-A is 5/4 times perimeter of a square. Area of the square is 961 sq. cm. What is the area of another circle-B whose diameter is half the radius of the circle-A?a)167.3 sq cmb)125.8 sq cmc)118.9 sq cmd)181.2 sq cme)None of theseCorrect answer is option 'C'. Can you explain this answer?
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Circumference of a circle-A is 5/4 times perimeter of a square. Area of the square is 961 sq. cm. What is the area of another circle-B whose diameter is half the radius of the circle-A?a)167.3 sq cmb)125.8 sq cmc)118.9 sq cmd)181.2 sq cme)None of theseCorrect answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Circumference of a circle-A is 5/4 times perimeter of a square. Area of the square is 961 sq. cm. What is the area of another circle-B whose diameter is half the radius of the circle-A?a)167.3 sq cmb)125.8 sq cmc)118.9 sq cmd)181.2 sq cme)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Circumference of a circle-A is 5/4 times perimeter of a square. Area of the square is 961 sq. cm. What is the area of another circle-B whose diameter is half the radius of the circle-A?a)167.3 sq cmb)125.8 sq cmc)118.9 sq cmd)181.2 sq cme)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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