# If the Circumference of a Circle and the Perimeter of a Square Are Equal, Then - Mathematics

MCQ
Sum

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)

• none of these

#### Solution

Area of the circle > Area of the square

Let r be the radius of the circle.

We know:

Circumference of the circle

= 2πr

Now,

Let a be the side of the square.
We know:
Perimeter of the square = 4a

Now,

2pi"r"=4"a"

=>"r" = (4"a")/(2pi)

∴ Area of the circle = πr2

=pixx((4"a")/(2pi))^2

=pixx(16"a"^2)/(4pi^2)

=(4"a"^2)/pi

=(4xx7"a"^2)/22

=(14"a"^2)/11

Also,

Area of the square = a2

clearly,(14"a"^2)/11 > "a"^2

∴ Area of the circle > Area of the square

Is there an error in this question or solution?

#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Multiple Choice Questions | Q 13 | Page 847