Question

what is the radius of a circle which touches all side of a square. if the Area of the square is 100 cm​

Answer 1

Given :-

• Area of the square is 100 cm²

To Find :-

• What is the radius of a circle which touches all side of a square ?  

Solution :-

~Here, we’re given the area of a square in which a circle is inscribed and we need to find the radius of that circle which touches all sides of that square. Firstly we’ll find the side of the square by putting the values in the formula of area and the side of square is equal to diameter of the circle. We can easily find the radius by dividing the diameter by 2.

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As we know that,

✰ Area of Square = Side × Side

✰ r = Diameter/2

Where,

• r is radius

Here,

✰ Side of square  = Diameter of circle

Finding the side :-

↬ Side × Side = 100 cm²  

↬ Side = √100 cm²  

↬ Side = √10 cm × 10 cm  

↬ Side = 10 cm  

Finding the radius :-

↬ Radius = Diameter/2  

↬ Radius = 10/2  

↬ Radius = 5 cm  

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Hence,  

• Radius of the circle is 5 cm

Answer 2

To do this I will assume that the circle is inside the square, touching the sides.

area of square = length * width

100 = length * width

and since it is a square, the length and width are the same ( call them both y )

100=y * y

so y is 10

so the width and length are 10, this also means the diameter of the circle is 10 (if it is touching the side of the square)

diameter = 10

area of a circle is pi * radius ^2

radius is half diameter

$\bold \color{red}{radius = 5}$

area = pi* 5^2

area =25 pi