Question

a wire is bent into the shape of a square the area of the square is 49 CM square when the wire is bent into a semicircular shape find the radius of the semicircle

Answer 1

Area of square = 49 cm
a^2 = 49
a= 7 cm

Side of square = 7 cm
Perimeter of square = Perimeter of semi circle
Perimeter of semi circle = 4* 7 = 28 cm

pi * r + 2r = 28
=> r (2+ pi) = 28
=> r (2+22/7) = 28
=> r (36/7) = 28
=> r = 28 * 7/36
=> r = 7*7/9
=> r = 49/9 cm

Radius of semi circle = 49/9
= 5.44 cm

Answer 2

Given Area of square = 49cm.

We know that Area os square = a^2.

a^2 = 49

a = 7cm.


We know that perimeter of square = 4 * a

                                                           = 4 * 7

                                                           = 28cm.



Then,

the perimeter of semicircle = pir + 2r

pir + 2r = 28

r(pi + 2) = 28

r(22/7 + 2) = 28

36/7 * r = 28

36 r = 196

r = 196/36

r = 5.4cm.