CAT Practice : Mensuration

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Area of a square inscribed.

Concentric Circles

    Q.16: There are 5 concentric circles that are spaced equally from each other by 1.25 cms. 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?
    1. 324 sq. cm.
    2. (66 + 40√2) sq. cm.
    3. 210.125 sq. cm.
    4. 162 sq.cm.

 

  • Correct Answer
    Choice D. 162 sq.cm.

Detailed Solution

Diagram -



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 8 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

Choice (D) is therefore, the correct answer.

Correct Answer: 162 sq. cm.



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Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.