Question

a wire which is bent to form a square encloses an area of 49 CM square.if the same wire is bent to form a circle, find the circumference of the circle and the area it will enclose

Answer 1

since area of square = side^2
=> side = sqrt (area)
=> side = sqrt (49)
=> side = 7 cm

perimeter of square = 4 × side
= 4 × 7 cm
= 28 cm

we know that perimeter of square = circumference of circle

therefore circumference of circle = 28 cm

since circumference of circle = 2 × pi × r
28 cm = 2 × pi × r
28 cm = 2 × 22/7 × r
r = 28 × 7 / 44
r = 49/11 cm (approx)

now area of circle = pi × r^2
= 22/7 × (49/11)^2
= 686 / 11 cm2
or 62.363 cm2
or 62.37 cm2