CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

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 :-
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

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

∴ 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.