If area of a square is 44 cm2, find the area of the circle formed by the same perimeter.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 56 cm2
“Formed by the same perimeter” means a wire bent into the square is bent again into a circle, so the circumference of the circle equals the perimeter of the square.
Side of the square \(=\sqrt{44}\) cm, so perimeter \(=4\sqrt{44}\) cm
\(2\pi r=4\sqrt{44}\), so \(\displaystyle r=\frac{2\sqrt{44}}{\pi}\)
Area of the circle \(\displaystyle =\pi r^2=\pi\times\frac{4\times44}{\pi^2}=\frac{176}{\pi}\)
\(\displaystyle \frac{176}{\pi}=176\times\frac{7}{22}=56\) cm2
Tip: For the same perimeter, a circle always encloses more area than a square (here 56 against 44 cm2), so Options (2) and (4), smaller than 44, can be struck out at once.