Circumference of circle = perimeter of square. Circle area is?
- Equal
- Less than
- Greater than
- None of these
Explanation
Let the circumference of the circle = perimeter of the square = P
- Circumference of circle = 2πr
- Perimeter of square = 4a (a = side of square)
So, 2πr = 4a ⇒ a = (πr)/2
- Area of circle = πr²
- Area of square = a² = (πr/2)² = (π²r²)/4
Now compare:
πr² (circle) vs. (π²r²)/4 (square)
Divide both sides:
(πr²) / ((π²r²)/4) = 4/π > 1 ⇒ area of circle > area of square.
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