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The difference in the area of a square of perimeter $88$ m and a circle with same circumference is

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133

c m^{2}

132

c m^{2}

122

c m^{2}

166

c m^{2}

answer is D.

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Detailed Solution

It is given to find the difference in the area of a square of perimeter

88

m and a circle with same circumference.
Perimeter of square

= 88 cm

∴

Side of square

= 22 cm

So the area of square

= π r^{2} = {484 cm}^{2}

and the circumference

C = 4 r = 88

cm.
Now

2 πr = 88

\Rightarrow πr = 44

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

\Rightarrow r = 14

So the radius of the circle is 14 cm.

∴

area of the circle will be

π r^{2}

\Rightarrow \frac{22}{7} \times 14 \times 14

\Rightarrow {616 cm}^{2}

Difference in the areas

= 616 - 484 = {132 cm}^{2}

.
Therefore, difference in the area of a square and circle is 132 sq. cm
Hence, option 4 is correct.

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