CAT Practice : Mensuration

You are here: Home  CAT Questionbank   CAT Quant  Geometry: Mensuration  Question 16
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


  • Correct Answer
    Choice D. 162

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.

Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play

More questions from Mensuration

  1. Cone and Frustum
  2. Spheres
  3. Circles and Chords
Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.