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  • If the perimeter of a circle is equal to that of a square, then the ratio of their areas is (A) 22 : 7 (B) 14 : 11 (C) 7 : 22 (D) 11: 14

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

(A) 22 : 7                    (B) 14 : 11                     (C) 7 : 22                    (D) 11: 14

Answers (1)

Answer(B) 14 : 11

Solution

According to question

2 \pi r=4a                 (Because perimeter of circle = 2πr   Perimeter of square =4 \times side)

\pi r=2a               (here side of square =a)

a=\frac{\pi r}{2}\\\\ \therefore \frac{Area \; of \; circle}{Area \; of\; square}=\frac{\pi r^{2}}{\left (\frac{\pi r}{2} \right )^{2}}=\frac{\pi r^{2}}{\pi r^{2}}\times \frac{4}{\pi}=\frac{4 \times 7}{22}=\frac{14}{11}  (Using area of square = a2)

 Hence ratio of their areas is 14: 11

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