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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

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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?
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APPEARS IN

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