CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

CAT Questions | CAT Mensuration Questions | Circle

This question is from CAT Mensuration in CAT Geometry. In this question, three circles of equal radius touch each other and we need to find the area of the circle. 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. Its's another interesting question that tests the understanding in properties of triangle.

Question 15: Three circles with radius 2 cm touch each other as shown :- CAT : Geometry: Mensuration; Circles
Find the area of the circle, circumscribing the above figure.

  1. 3π(4 + √3)2
  2. \\frac{π}{3}\\) (4 + 2√3)2
  3. \\frac{π}{4}\\) (4 + 2√3)2
  4. 12π - \\frac{π}{2}\\) (4 + 2√3)2

2IIM : Best Online CAT Coaching

Signup and sample 9 full classes for free
The Best CAT Online Coaching Courses

Best CAT Coaching in Chennai

CAT Coaching in Chennai - CAT 2020
Starts Sun, March 1st, 2020

Explanatory Answer

Method of solving this CAT Question from Geometry - Mensuration: Let's go with the given details by assuming r’ as the circumradius of ∆ABC

CAT : Geometry: Mensuration; Circles
∴ R = 2 + r’
We know from the properties of equilateral triangle,
r’ = \\frac{Sides}{√3}\\) = \\frac{4}{√3}\\)
(This can easily be derived using trigonometry. However, please remember this formula. It is useful at places)
∴ R = 2 + \\frac{4}{√3}\\)
∴ Area = π * R2 = π * \\frac{(2√3 + 4)^2}{√3^2}\\)
= \\frac{π}{3}\\) * (4 + 2√3)2

The question is " Find the area of the circle, circumscribing the given figure. "

Hence, the answer is \\frac{π}{3}\\) (4 + 2√3)2

Choice B is the correct answer.


CAT Preparation Online | CAT Geometry - Mensuration Videos On YouTube

Other useful sources for Geometry Questions | Mensuration Questions

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT

Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now