Question

A wire 44cm long is bent to form a square. A ribbon 44 cm long is made to form a circular ring. Which encloses more area and by how much?

Answer 1

Case 1 :
A wire 44 cm long is bent to form a square of side, s.
Length of a wire, l = Perimeter of a square = 4(s)
44 cm = 4.s
s = 44/4 = 11 cm.
Area of a square = s² = (11)² = 121 cm²

Case 2 :
A ribbon 44 cm long is made to form a circular ring of radius, r.
Length of the ribbon, l = Circumference of the ring = 2πr
44 cm = 2πr = 2(22/7).r
r = 7 (44) / 44 = 7 cm.
Area of a circular ring = πr² = (22/7)(7)² = 154 cm²           

The area of the circular ring is greater than the area of the square and hence, the ribbon made to form a circular ring encloses more area.

As, (154 - 121) is equal to 33, the areas vary by a difference of 33 cm².

Answer 2

ATQ  The perimeter of square = 44 cm
         Side of the square is 44/4= 11 cm
         Hence the area = 11²= 121 cm²
Circumference of ring = 2πr = 44 cm
            That gives radius  r = 7 cm
Area enclosed by ring= πr²= 22*7²/7= 154 cm²
Ring encloses more area by 154-121=33 cm²