A wire is bent to form a square of area 169 cm2 . If the same wire is bent to form circle, then what is its area (in cm2 , to the nearest whole number)?
Take $π = \frac{22}{7}$
Answer & explanation
Correct answer: option 1
Area of square = ( Side )²
169 = ( Side )²
Side = 13 cm
Now, Same wire that is used to form square is used to form circle.
So, Perimeter of square = Perimeter of Circle
Perimeter of square = 4 × Side = 4 × 13 = 52 cm
Now, Perimeter of circle = 2πR
= 2 × \(\frac{22}{7}\) × R
2 × \(\frac{22}{7}\) × R = 52
R = \(\frac{52 × 7 }{22 × 2 }\)
= \(\frac{91 }{11 }\)
Area of circle = πR²
= \(\frac{22}{7}\) × \(\frac{91 }{11 }\) × \(\frac{91 }{11 }\)
= 215.09 cm²