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Q.

Two circular pieces of equal radii and maximum area, touching each other are cut out from rectangular cardboard of dimensions 14 cm × 7 cm. Find the area of the remaining cardboard. [Use π= 22 7  ]


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a

      27c m 2  

b

23c m 2  

c

25c m 2  

d

21c m 2   

answer is D.

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Detailed Solution

Given that two circular pieces of equal radii and maximum area, touching each other are cut out from rectangular cardboard of dimensions 14 cm × 7 cm.
We have to find the area of the remaining cardboard.
The area of a circle can be expressed as A=π r 2   where is the radius of a circle.
The required figure geometry is shown below,
Class 10 RD Sharma Solutions - Chapter 15 Areas Related to Circles - Exercise 15.4 | Set 2 - GeeksforGeeksFrom the figure, the diameter of the circles is d.
Then, the area of the remaining cardboard, As by using the figure geometry is,
     A s = π 4 d 2 + π 4 d 2 − l b ⇒ A s = π 4 7 2 + π 4 7 2 − 14 7 ⇒ A s =98−77 ⇒ A s =21  cm 2  
The area of the remaining cardboard is 21c m 2 .  
Therefore, the correct option is 4.
 
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