Circle And System Of Circles Question 217
Question: If a circle and a square have the same perimeter, then
[Pb. CET 2001]
Options:
A) Their area are equal
B) Area of circle is larger
C) Area of square is larger
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We are given that, the perimetre of the circle is equal to the perimetre of square.
$ \therefore $ Let -r- be the radius of circle and -a- be the side of square
$ \therefore $ $ 2\pi ,r=4a\Rightarrow a=\frac{\pi ,r}{2} $
$ \therefore $ Area of square
$ \Rightarrow $ $ a^{2}=\frac{{{\pi }^{2}}r^{2}}{4} $ and area of circle = $ \pi ,r^{2} $
$ \therefore $ $ \frac{\text{Area of circle}}{\text{Area of square}}=\frac{\pi ,r^{2}}{{{\pi }^{2}}r^{2}/4}=\frac{4}{\pi }>1 $ . Thus, area of circle is larger than area of square.
BETA
