CAT 1996 — QA Question 5
Basics of Mensuration/PrismEasy
Passage / Data
Direction: Answer the questions based on the following information.
In a locality, there are five small cities: A, B, C, D and E. The distances of these cities from each other are as follows.
AB = 2 km AC = 2km AD > 2 km AE > 3 km BC = 2 km
BD = 4 km BE = 3 km CD = 2 km CE = 3 km DE > 3 km
From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?
Answer & solution
- A
1 : 3
- B
4 : 1
3 : 1
- D
4 : 3
Solution
Area of the original paper = π(20)2 = 400π cm2. The total cut portion area = 4(π)(5)2 = 100π cm2 . Therefore, area of the uncut (shaded) portion = (400 – 100) = 300π cm2.
Hence, the required ratio = 300π : 100π = 3 : 1.