If the circumference of a circle is equal to the perimeter of a square, and the radius of the given circle is positive, then which of the following options is correct?
Answer & explanation
Correct answer: option 1
We know that,
Area of circle = πr2
Circumference of circle = 2πr
Perimeter of square = 4a
Area of square = a2
According to the question,
2πr = 4a
2 × \(\frac{22}{7}\) × r = 4a
\(\frac{44}{7}\) × r = 4a
\(\frac{r}{a}\) = \(\frac{7}{11}\)
Now the area of circle = πr2 = \(\frac{22}{7}\) × 7 × 7 = 154
The area of square = a2 = 112 = 121
So we can clearly see that Area of the circle > Area of the square