question_answer

A circular paper is folded along its diameter; then again it is folded to form a quadrant. Then it is cut as shown in the figure and after that the paper was reopened in the original circular shape. What is the ratio of the original paper to that of the remaining paper? (The shaded portion is cut off from the quadrant. The radius of quadrant OAB is 5 cm and radius of each semicircle is 1 cm):

A)  \[25:16\]       

B)  \[25:9\]        

C)  \[20:9\]                        

D)  \[31:25\]

Correct Answer: A

Solution :

(a):   When we open the paper after cutting it, we will find it as shown in the following figure. Radius of the larger circle = 5cm Area of larger circle \[=25\pi \] and the radius of each smaller circle is 1 cm. Therefore, total areas of all the 9 circles \[=9\times \pi \times \left( {{1}^{2}} \right)=9\pi \] Hence, the required ratio \[=25:16\]