Question

If the circumference of a circle and the perimeter of a square are equal, then
A. Area of the circle = Area of the square
B. Area of the circle `gt` Area of the square
C. Area of the cirlce `lt` Area of the square
D. Nothing definite can be said about the between the areas of the circle and square

Answer 1

Correct Answer - B
Accordign to the given condition,
Circumterence of a circle = Perimeter of square
`2pi ` r = 4a
[where, r and a are radius of circle and side of square respectively]
`rArr (22)/(7)r = 2a rArr 11r = 7a`
`rArr a =(11)/(7)r rArr r=(7a)/(11)` ....(i)
Now, area of circle, `A_(1) = pir^(2)`
= `pi((7a)/(11))^(2)=(22)/(7)xx(49a^(2))/(121)` [from Eq. (i)]
= `(14a^(2))/(11)` ...(ii)
and area of square, `A_(2)= (a)^(2)` ...(iii)
From Eqs. (ii) and (iii), `A_(1)= (14)/(11)A_(2)`
`:. A_(1) gt A_(2)`
Hence, Area of the circle `gt` Area of the square.