CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

CAT Questions | CAT Mensuration Questions | Concentric Circles

This question is from CAT Mensuration in CAT Geometry. Five circles which are equally spaced and have same centre is given. Area of a square inside the smaller circle is known and we need to relate it with the bigger circle to find area of a square inside it. Mensuration Questions in the CAT exam can be solved with practical approach and thought process rather than just knowing theorems from CAT Geometry. Even if one is not completely prepared for CAT Geometry exam, he or she should be able to do well in Mensuration problems tested by the CAT Exam. Knowing Mensuration formulas is important. Make sure you master Mensuration questions for CAT exam.

Question 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.

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Explanatory Answer

Method of solving this CAT Question from Geometry - Mensuration: Once you visualize it, you are through!

CAT : Geometry: Mensuration; Circles
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

The question is " If a square needs to be inscribed in the outermost circle, what will be its area? "

Hence, the answer is 162

Choice D is the correct answer.


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