# If the perimeter of a circle is equal to that of a square, then the ratio of their areas is ______. - Mathematics

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

•  13 : 22

• 14 : 11

•  22 : 13

• 11 : 14

#### Solution

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is 14 : 11.

Explanation:

Let radius of circle be r and side of a square be a.

Perimeter of a circle = Perimeter of a square

∴ 2pir = 4a

⇒ a = (pir)/2  .....(i)

Now, "Area of circle"/"Area of square" = (pir^2)/(a)^2 = pi^2/((pir/2)^2  ......[From equation (i)]

= (pir^2)/((pi^2r^2)/4) = 4/pi

= 4/(22/7) = 28/22

= 14/11

Concept: Area of Circle
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 13 Areas Related to Circles
Exercise 13.6 | Q 39 | Page 73
NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.1 | Q 5 | Page 121

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