# 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?

2
by charlotteds9

2015-01-07T10:09:31+05:30

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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.
2015-01-07T17:15:11+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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