A copper wire of length 44 cm is to be bent into a square and a circle. Which will have a larger area?

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Solution

(i) When the wire is bent into a square.

Side $= \frac{44}{4} = 11$ cm

Area of the square $= (s i d e)^{2} = (11)^{2} = 121 c m^{2}$

(ii) When the wire is bent into a circle.

Circumference $= 2 π r$

$44 = 2 π r$

$44 = 2 \times \frac{22}{7} \times r$

$r = \frac{44 \times 7}{22 \times 2} = 7$ cm

Area of circle $= π r^{2}$

$= \frac{22}{7} \times 7 \times 7 = 154 c m^{2}$

So, the circle will have a larger area.

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A copper wire of length 44 cm is to be bent into a square and a circle. Which will have a larger area?

(i) When the wire is bent into a square. Side =444=11 cm Area of the square =(side)2=(11)2=121 cm2 (ii) When the wire is bent into a circle. Circumference =2πr 44=2πr 44=2×227×r r=44×722×2=7 cm Area of circle =πr2 =227×7×7=154 cm2 So, the circle will have a larger area.