Question

If a wire is bent into the shape of a square the area of the square is 49cmsquare . when the wire is bent into a semi circular shape. Find the radius of the semi circle.take pie 22by 7

Answer 1

Answer :

Given : A wire is bent into the shape of a square the area of the square is 49 cm²

Let side of square = x

We know area of square = ( Side )² , So

x² = 49

x = 7 cm

We know perimeter of square = 4 ( Side )
So,

Perimeter of square = 4 ( 7 ) = 28 cm

And Length of wire = Length of wire

So,
Length of wire = 28 cm

As given : The wire is bent into a semi circular shape .

So,

Perimeter of semicircular shape = 28 cm

We know Perimeter of semicircle = $2\mathrm{\pi }r+2r$ , Here r is radius

So,
$$\begin{gathered} 2\mathrm{\pi }r+2r=28 \\ \Rightarrow 2\times \frac{22}{7}\times r+\hspace{0.17em}2r=28 \\ \Rightarrow \frac{44}{7}\times r+\hspace{0.17em}2r=28 \\ \Rightarrow r\left(\frac{44}{7}+\hspace{0.17em}2\right)=28 \\ \Rightarrow r\left(\frac{44+14}{7}\right)=28 \\ \Rightarrow r\left(\frac{58}{7}\right)=28 \\ \Rightarrow r=\frac{28\times 7}{58} \\ \Rightarrow r=\frac{196}{58} \\ \Rightarrow r=3.379cm\approx \mathbf{}\mathbf{3}\mathbf{.}\mathbf{38}\mathbf{}\mathit{c}\mathit{m}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{}\mathit{A}\mathit{n}\mathit{s}\mathbf{}\mathbf{)} \end{gathered}$$