CAT 1996 | Question: 106

Question

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?

• A. $1:3$ 
• B. $4:1$ 
• C. $3:1$
• D. $4:3$

Answer 1

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.