Question

If the circumference of a circle is equal to the perimeter of a square what is the ratio of the area of the circle to the area of the square?

• A. $4:1$
• B. $11:7$
• C. $22:7$
• D. $14:11$

Answer 1

Answer: (D)

Let perimeter of square $=4s$
Let perimeter of circle $=2\pi r$
we have $4s=2\pi r$ since the perimeters of both the square and the circle are equal
This makes $s=\frac{2\pi r}{4}$
area of square equals $=s^2={\left(\frac{2\pi r}{4}\right)}^2=\frac{4{\pi }^2{r}^2}{16}$
area of circle equals $=\pi r^2$
ratio of area of circle to area of square equals $=\frac{16\pi r^2}{4{\pi }^2{r}^2}=\frac{4}{\pi }=\frac{7\times 4}{22}=\frac{14}{11}$