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Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also, find its area, If the same wire is bent into the shape of a square, what will be the length of each of its sides?

Q. 9.     Shazli took a wire of length 44\; cm and bent it into the shape of a circle. Find the radius of that circle. Also, find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Take \pi =\frac{22}{7} )

Answers (1)
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It is given that the length of wire is 44 cm

Now, we know that

Circumference of the circle (C) = 2 \pi r

\Rightarrow 44 = 2 \pi r

\Rightarrow r = \frac{44\times 7}{2 \times 22} = 7 \ cm

Now,

Area of circle (A) = \pi r^2

\Rightarrow \pi r^2= \frac{22}{7}\times (7)^2= 154 \ cm^2                                      - (i)

Now,

Perimeter of square(P) = 4a

\Rightarrow 44=4a

\Rightarrow a = \frac{44}{4} = 11 \ cm

Area of sqaure = a^2

\Rightarrow a^2 = (11)^2= 121 \ cm^2                                                   -(ii)

From equation (i) and (ii) we can clearly see that area of the circular-shaped wire is more than square-shaped wire 
 

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