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CAT 1996 | Question: 106

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From a circular sheet of paper with a radius of 20 cm, four circles of radius 5cm each are cut out. What is the ratio of the paper left to the area of the circles?

  1. $1:3$ 
  2. $4:1$ 
  3. $3:1$
  4. $4:3$

1 Answer

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Area of the circular sheet = $\pi$ * (20)2 = 400 $\pi$

Area of 4 smaller circles cut out = 4 * $\pi$ * (5)2 = 100 $\pi$

So, area of remaining paper = 300 $\pi$

$\therefore$ Ratio of the paper left to the area of the circles = 300 $\pi$ : 100 $\pi$ = 3 : 1

C is the answer.

 

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