Question

a wire of length 66 cm is bent into the shape of a circle . find its area. if the same wire is bent into the shape of a square, what will be its area? which figure enclose more area, the circle or the square?take π22/7.

Answer 1

length of wire = circumference of circle
66 = 2πr
21/2 = r

Now, area = πr^2
= 22/7 x 21/2 x 21/2 = 346.5 unit sq.

length of wire = perimeter of square
66 = 4xa
a = 16.5

area of square = 272.5 unit square.

Hence, circle encloses more area.

Answer 2

Circumference of the circle = 2πr
2πr = 66 cm
2×22/7× r = 66 cm
22/7 × r = 66/2 = 33
r = 33 × 7/22
r = 231 / 22
r = 10.5
Area of the circle = π (radius)2
= 22/7 × 10.52
= 22/7 × 110.25
= 22×110.25/7
= 346.5
perimeter of the square = 4a
4a = 66 cm
4 × a = 66 cm
a = 66/4
a = 16.5
Area of the square = a2
a2 = 16.52
= 272.25
Ans : The circle enclose more area