9. If the perimeter of a circle is equal to that of a square then find the ratio of their areas
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sayliujawane
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meenuwin
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perimeter of circle = 2π r
perimeter of square = 4a
a = diameter of circle (d)
so,
πd = 4a
ratio of areas,
π r^2 : d^2 (because, a = d) ---------- (1)
r = d/2
substituting, r value in π r^2, we get,
π × (d/2)^2
= π × d^2/4
now, from (1)
π d^2/4 : d^2
so,
π d^2/4 ÷ d^2
= π d^2/4 × 1/d^2 (where, d^2 will get cancelled)
= π/4 × 1 -------- (2)
substituting π value in (2),
= 22/7 ÷ 4
= 22/7 × 1/4
= 22/28 (using 2 as the common divisor, we divide 22 and 28 to get 11 and 14 respectively)
=11/14
therefore, ratio of areas = 11 :
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Answer:
π÷4
Step-by-step explanation:
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