Mathematics What is the maximum possible radius of a circle that can be fitted inside a square of side ‘a’ unit.

 What is the maximum possible radius of a circle that can be fitted inside a square of side ‘a’ unit.


  1. A
    a 2  
  2. B
    a 3  
  3. C
    a 4  
  4. D
    a 5   

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    Solution:

    IMG_256
    Here we see the largest circle that can be placed in a square of side "a". If we increase the radius of the circle, then the circle will come out of the square and will no longer fit into the square.
    In a circle, the largest line segment that can be measured is known as the diameter.
    We know that the Diameter is the length of the line passing through the center that touches two points on the edge of the circle.
    In the diagram we can see that the diameter of the circle will be equal to unit "a".
    So average =
    As we know there is a relationship between diameter and radius.
    relationship is
    diameter=2×(radius)  
    If we put the value of the diameter into this relationship, we can find the radius of the circle.
    After entering the value of the average into the relationship, we get
    diameter=2×(radius) a=2×(radius) radius= a 2  
    Hence, we can say that the maximum radius of a circle which can be fitted in the square of side ‘a’ unit is  a 2  .
    So, option 1 is correct.
    IMG_256 
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