Question

Determine the area of circle whose circumference is equal to the perimeter of a square of side $44cm$ $(\text{Take}\pi =\frac{22}{7})$.

• A. $1232c{m}^2$
• B. $1210c{m}^2$
• C. $600c{m}^2$
• D. $626c{m}^2$

Answer 1

The correct option is A $1232c{m}^2$

Given: Circumference of circle $=$ Perimeter of square

Side of square $=44cm$

Circumference of a circle $=2\pi r$

Perimeter of square $=4\times side$

$2\pi r=4\times 44$

$2\times \frac{22}{7}\times r=4\times 44$

$\frac{2\times 22\times r}{22\times 7}=\frac{4\times 44}{22}$

$\frac{2r}{7}=8$

$\frac{2r}{7}\times 7=8\times 7$

$2r=56$

$r=28cm$

Area of the circle $=\pi r^2$

$=\frac{22}{7}\times 28\times 28$

$=22\times 4\times 28$

$=88\times 28$

$=1232c{m}^2$