Question

Given that the circle is inscribed in the given square,what is the ratio of the circumference of the circle to the perimeter of the square?

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{5}$

Answer 1

The correct option is C $\frac{\pi }{4}$

Perimeter of a square $=4s$
Circumference of a circle $=2\pi r$
$\text{Ratio}=\frac{2\pi r}{4s}$
$=\frac{2\pi \times 5}{4\times 10}$
$=\frac{10\pi }{40}$
$=\frac{\pi }{4}$