MCQ
If a square and a circle have the same perimeter then:
  • The area of the circle is greater than that of square.
  • B
    The area of the square is greater than that of circle.
  • C
    The area of the square is $\frac{1}\pi$ times that of the circle.
  • D
    Their areas are equal.

Answer

Correct option: A.
The area of the circle is greater than that of square.

Let the perimeter of circle and square is $1$Then perimeter of circle $={2}\pi\text{r}$
$= 1$ (wherer is redius of circle) $\Rightarrow\text{r}=\frac{1}{2\pi}$
Then area of circle $ = \pi\text{r}^{2} = \pi(\frac{1}{2\pi})^{2} = \frac{1}{4\pi} = 0.0789$
perimeter of square $= 4l = 1$ then l $= \frac{1}{4}$ (where l id the side of square)
Then area of square $=\frac{1}{4}\times\frac{1}{4} = \frac{1}{16} = 0.0625$
Then area of circle is greater then that of squre

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free