# If the circumference of a circle and the perimeter of a square are equal , then ______. - Mathematics

MCQ
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If the circumference of a circle and the perimeter of a square are equal, then ______.

#### Options

• Area of the circle = Area of the square

• Area of the circle  < Area of the  square

• Area of the circle > Area of the square

• Nothing definite can be said about the relation between the areas of the circle and square.

#### Solution

If the circumference of a circle and the perimeter of a square are equal, then Area of the circle > Area of the square.

Explanation:

Circumference of a circle = Perimeter of square

2pir = 4a  .....[Where r and a are radius of circle and side of square respectively]

⇒ 22/7 r = 2a

⇒ 11r = 7a

⇒ a = 11/7 r

⇒ r = (7a)/11  ......(i)

Now, Area of circle, A_1 = pir^2

= pi((7a)/11)^2 = 22/7 xx (49a^2)/121  .....[From equation (i)]

= (14a^2)/11  ......(ii)

And Area of square, A_2 = (a)^2  .....(iii)

From equations (ii) and (iii), A_1 - 14/11 A_2

∴ A_1 > A_2

Hence, Area of the circle > Area of the square.

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 52 | Page 74
NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.1 | Q 3 | Page 121

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