CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

This question is from CAT Mensuration in CAT Geometry.In this question, there is a circle in which some more circles are drawn inside and based on the given condition we need to answer. 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. This question requires a bit of visualization and the ability to express one area in terms of another.

Question 12: PQRS is a circle and circles are drawn with PO, QO, RO and SO as diameters areas A and B are shaded A/B is equal to

1. π
2. 1
3. \\frac{π}{4}\\)
4. 2

Explanatory Answer

Method of solving this CAT Question from Geometry - Mensuration: In these kind of questions, ability to visualize and to write one area in terms of others will hold the key.

Here,
Let the radius of PQRS be 2r
∴ Radius of each of the smaller circles = \\frac{2r}{2}\\) = r
∴ Area A can be written as
A = π (2r)² – 4 x π(r)² (Area of the four smaller circles) + B (since, B has been counted twice in the previous subtraction)
=> A = 4πr² - 4πr² + B
=> A = B
=> \\frac{A}{B}\\) = 1

The question is " PQRS is a circle and circles are drawn with PO, QO, RO and SO as diameters areas A and B are shaded A/B is equal to "

Hence, the answer is 1

Choice B is the correct answer.