Question

Find the area of a circle whose circumference is same as the perimeter of a square of side 88cm
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Answer 1

Given :

Side of a square is 88 cm .

To Find :

Area of circle whose circumference is same as the perimeter of square .

Solution :

For Finding the Area of Circle , we need to find the Perimeter of Square . Therefore ,

Formula :

$\longmapsto\sf{Perimeter\:of\:Square=4\times{Side}}$

Subsituting Values :

$\longmapsto\sf{4\times{88}}$

$\longmapsto\sf{352}$

Therefore , Perimeter of Square is 352 cm .

Now ,

As circumference of circle is same as the perimeter of a Square . Therefore ,

Formula :

$\longmapsto\sf{Circumference\:of\:Circle=2\pi{r}}$

Subsituting Values :

$\longmapsto\sf{352=2\times\dfrac{22}{7}\times{r}}$

$\longmapsto\sf{352\times{7}=44\:r}$

$\longmapsto\sf{2464=44\:r}$

$\longmapsto\sf{r=\dfrac{2464}{44}}$

$\longmapsto\sf{r=56\:cm}$

For Area :

$\longmapsto\sf{Radius=56\:cm}$

Formula :

$\longmapsto\sf{Area\:of\:Circle=\pi{{r}^{2}}}$

Subsituting Values :

$\longmapsto\sf{\dfrac{22}{7}\times{56}\times{56}}$

$\longmapsto\sf{22\times{8}\times{56}}$

$\longmapsto\sf{9856\:{cm}^{2}}$

Answer 2

GIVEN :

• Side of a square = 88 cm.

TO FIND :

• Area of circle whose circumference is same as the perimeter of square.

FORMULAS USED :

• Perimeter of square = 4 × side.
• Circumference of circle = 2 πr.
• Area of circle = πr².

SOLUTION :

First, we need to find the perimeter of square,

$\leadsto$ perimeter of square = 4 × side.

Now, substituting the values,

we get,

$\implies \sf 4 \times 88$

$\implies$ 352

$\therefore$ Perimeter of square is 352 cm.

Now,

Using circumference of a circle = 2πr

Substitue the values in the above formula.

we get,

$\implies \sf 352 \: = \: 2 \times \dfrac {22}{7} \times r$

$\implies \sf 352 \times 7 \: = \: 44 r$

$\implies \sf 2464 \: = \: 44 r$

$\implies \sf r \: = \: \dfrac {2464}{44}$

$\implies \sf r \: = \: 56 \: cm$

For Area :

$\leadsto \sf Radius \: = \: 56 \: cm$

Now,

Using Area of circle = πr².

Substitute the values in the above formula.

we get,

$\implies \sf \dfrac {22}{7} \times 56 \times 56$

$\implies \sf 22 \times 8 \times 56$

$\implies \sf 9856 \: cm^{2}$