CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

CAT Questions

This question is from CAT Mensuration in CAT Geometry. A string is would around two circular disks. Radii of the disks are given and we need to find out the length of the string. 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 6: A string is wound around two circular disk as shown. If the radius of the two disk are 40 cm and 30 cm respectively. What is the total length of the string?

1. 140 + 45π cm
2. 140 + 165π cm
3. 140 + 120π cm
4. 140 + 165π/2 cm

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Explanatory Answer

Method of solving this CAT Question from Geometry - Mensuration: What is the relation between length of the string and a Circle ( p.s. it has something do with the circumference!!).

As, tangent from an exterior point makes right angle with the radius.
=> ADXB and ODX’E are squares,
∴ AO = BO = 40 cm
OD = DE = 30 cm
Length of string wound around circle x => 270^°/360^° ∗ 2 ∗ π ∗ 80
= 3/4 ∗ 160π
=120π
Similarly, Length of string wound around circle x’ => 270^°/360^° ∗ 2 ∗ π ∗ 30
= 3/4 ∗ 30π
= 45π/2
∴ Length of the string = 80 + 60 + 120π + 45π/2 ∗ π
= 140 + 165π/2

The question is "What is the total length of the string?"

Hence, the answer is 140 + 165π/2 cm.

Choice D is the correct answer.