Question

If a wire of $440m$ length is moulded in the form of a circle and a square turn -by -turn find the ratio of the area of the area of the circle to that of square.

Answer 1

Given

$2\pi r=440$

$4a=440$

find

ratio of $\to \frac{areaofcircle}{areaofsquare}$

sol

$2\pi r=440$

$r=\frac{440}{2\pi }=\frac{220}{\pi }$

circle (Area) = $\pi r^2$

$=\pi \times \frac{220}{\pi }\times \frac{220}{\pi }$

$\Rightarrow \frac{(220{)}^2}{\pi }$

$4a=440$

$a=110$

Area sq = $a^2$

$=110\times 110$

$\therefore$ Ratio = $\frac{220\times 220}{\pi \times 110\times 110}$

$\Rightarrow \frac{4}{\pi }$ $[\because \pi =\frac{22}{7}]$

$\Rightarrow \frac{4}{22}\times 7=\frac{28}{22}$