Question

a 44 cm long wire is bent to form a square if the same wire is bent to make a circular ring which shape would have more area and by how much​

Answer 1

Step-by-step explanation:

Since wire is bent to a square,

Perimeter of square = 44cm

= 4 × side = 44cm

= side= 44/4

= side = 11cm

Area of square = side²

= (11cm)²

=121cm²

Now, wire is bent to a circular ring

i.e., Circumference = 44cm

=2×22/7 × radius = 44cm

=radius= 7 cm

Area of circle = pi × radius²

=22/7 × 7²

= 22× 7

= 154cm²

Therefore , circle has more area by

154cm² - 121cm²

=33cm²

Answer 2

Given:

perimeter of a square = 44cm

side = 44÷4(side × 4 = perimeter then perimeter ÷ 4 = side)

Area of ths square:

$area \: of \: square \: = side { \\ }^{2} \\ \: side \: = 11cm \\ 11 { \\ }^{2} = 121cm {}^{2}$

Radius of circle =

perimeter of square = perimeter/circumference of circle

so

44 = 2πr

$\frac{44 \times 7}{2 \times 22} = 7cm$

Area of the circle

$\pi \times {r}^{2} \\ \frac{22}{7} \times {7}^{2} = 154 {cm}^{2}$

Circle has the higher area than square

154>121

so

154 - 121

33cm

the area of the circle is bigger than square by 33cm