Question

-Q047: A silver wire when bent in the form of a square encloses an area of 4 cm square. Now if the same wire is bent to form a circle, the area enclosed by it would be approximately? ​

Answer 1

Answer:

The area of the circle enclosed by the wire is 5.0955cm².

Step-by-step explanation:

The silver wire is first bent to form a square.

The area of the square is 4cm².

Area of a square = (length of its side)²

∴ Length of the side = √(area)

                                  = √4cm²

                                  = 2cm.

Therefore the length of the side is 2cm.

Now length of the wire is same as the perimeter of the square.

Perimeter of the square = 4 × length of side

                                        = 4 × 2cm

                                        = 8cm.

Hence the length of the wire is 8cm.

Now, this wire is bent to form a circle. Then the perimeter of the circle is same as the length of the wire, which is 8cm.

Perimeter of a circle = $2\pi r$

                            $2\pi r=8$

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

                             $\pi r=4$

                              $r=\frac{4}{\pi }$.

We have to calculate the area of the circle.

Area of a circle = $\pi r^{2}$

                         = $\pi \times ({\frac{4}{\pi } )^2}$

                         = $\pi \times \frac{16}{\pi ^{2} }$

                         = $\frac{16}{\pi }$

                         = $\frac{16}{3.14}$

                         = $5.0955cm^{2}$.

That is, the area of the circle enclosed by the wire is 5.0955cm².