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There are 5 concentric circles that are spaced equally from each other by 1.25 cm. The innermost circle has a square of side √32 cm inscribed in it. If a square needs to be inscribed in the outermost circle, what will be its area?
- a)150 sq. cm
- b)152 sq. cm
- c)160 sq. cm
- d)162 sq. cm
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
There are 5 concentric circles that are spaced equally from each othe...
From the figure, we can see that the diagonal of the square inscribed in innermost circle is
the diameter of the innermost circle.
Side = √32
Or Diagonal = √32 × √2 = 8 cm
Since the circles are spaced at 1.25 cm, the distance between innermost and outermost
circles = 1.25 × 4 = 5 cm
Therefore the diameter of the outermost circle = 5 cm + diagonal of inscribed square + 5cm
= 18 cm
Now this 18 cm will be the diagonal of the square that needs to be inscribed in outermost
circle.
Or a√2 = 18
a = 9√2 cm
Area = 9√2 × 9√2 = 162 sq. cm
Hence, the correct option is (d).
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There are 5 concentric circles that are spaced equally from each othe...
Understanding the Problem
To find the area of the square inscribed in the outermost circle, we first need to understand the dimensions and relationships of the circles and the inscribed shapes.
Dimensions of the Innermost Circle
- The square inscribed in the innermost circle has a side length of √32 cm.
- The radius \( r_1 \) of the innermost circle can be found using the relationship between the side of the square and the radius:
- \( r_1 = \frac{\text{side length}}{\sqrt{2}} = \frac{\sqrt{32}}{\sqrt{2}} = \sqrt{16} = 4 \) cm.
Finding the Radius of the Outermost Circle
- There are 5 concentric circles, spaced equally by 1.25 cm:
- The radius of the outermost circle \( r_5 \) can be calculated as:
- \( r_5 = r_1 + 4 \times 1.25 = 4 + 5 = 9 \) cm.
Inscribing a Square in the Outermost Circle
- The radius of the outermost circle is 9 cm.
- The side length \( s \) of the square inscribed in this circle can be calculated using:
- \( s = r_5 \times \sqrt{2} = 9 \times \sqrt{2} \).
Calculating the Area of the Square
- The area \( A \) of the square is given by:
- \( A = s^2 = (9 \sqrt{2})^2 = 81 \times 2 = 162 \) sq. cm.
Conclusion
- Therefore, the area of the square inscribed in the outermost circle is 162 sq. cm. The correct answer is option D.
To find the area of the square inscribed in the outermost circle, we first need to understand the dimensions and relationships of the circles and the inscribed shapes.
Dimensions of the Innermost Circle
- The square inscribed in the innermost circle has a side length of √32 cm.
- The radius \( r_1 \) of the innermost circle can be found using the relationship between the side of the square and the radius:
- \( r_1 = \frac{\text{side length}}{\sqrt{2}} = \frac{\sqrt{32}}{\sqrt{2}} = \sqrt{16} = 4 \) cm.
Finding the Radius of the Outermost Circle
- There are 5 concentric circles, spaced equally by 1.25 cm:
- The radius of the outermost circle \( r_5 \) can be calculated as:
- \( r_5 = r_1 + 4 \times 1.25 = 4 + 5 = 9 \) cm.
Inscribing a Square in the Outermost Circle
- The radius of the outermost circle is 9 cm.
- The side length \( s \) of the square inscribed in this circle can be calculated using:
- \( s = r_5 \times \sqrt{2} = 9 \times \sqrt{2} \).
Calculating the Area of the Square
- The area \( A \) of the square is given by:
- \( A = s^2 = (9 \sqrt{2})^2 = 81 \times 2 = 162 \) sq. cm.
Conclusion
- Therefore, the area of the square inscribed in the outermost circle is 162 sq. cm. The correct answer is option D.
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There are 5 concentric circles that are spaced equally from each other by 1.25 cm. The innermost circle has a square of side √32 cm inscribed in it. If a square needs to be inscribed in the outermost circle, what will be its area?a)150 sq. cmb)152 sq. cmc)160 sq. cmd)162 sq. cmCorrect answer is option 'D'. Can you explain this answer?
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There are 5 concentric circles that are spaced equally from each other by 1.25 cm. The innermost circle has a square of side √32 cm inscribed in it. If a square needs to be inscribed in the outermost circle, what will be its area?a)150 sq. cmb)152 sq. cmc)160 sq. cmd)162 sq. cmCorrect answer is option 'D'. 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 There are 5 concentric circles that are spaced equally from each other by 1.25 cm. The innermost circle has a square of side √32 cm inscribed in it. If a square needs to be inscribed in the outermost circle, what will be its area?a)150 sq. cmb)152 sq. cmc)160 sq. cmd)162 sq. cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 5 concentric circles that are spaced equally from each other by 1.25 cm. The innermost circle has a square of side √32 cm inscribed in it. If a square needs to be inscribed in the outermost circle, what will be its area?a)150 sq. cmb)152 sq. cmc)160 sq. cmd)162 sq. cmCorrect answer is option 'D'. Can you explain this answer?.
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