Question

Area of a circle is same as that of a square of length 10 cm. The circumference of the circle is

• A. \(10\pi\) cm
• B. \(20\pi\) cm
• C. \(102\pi\) cm
• D. \(2012\pi\) cm

Answer 1

The Correct Option is B

Step 1: The area of the circle is equal to the area of the square. The area of the square is given by: \[ \text{Area of square} = \text{side}^2 = 10^2 = 100 \, \text{cm}^2. \] Step 2: The area of the circle is \( \pi r^2 \), where \( r \) is the radius. Thus, we can equate the area of the circle to the area of the square: \[ \pi r^2 = 100 \] Solving for \( r^2 \): \[ r^2 = \frac{100}{\pi} \] Taking the square root of both sides: \[ r = \sqrt{\frac{100}{\pi}} \] Step 3: The circumference of the circle is given by \( 2\pi r \). Substituting the value of \( r \): \[ \text{Circumference} = 2\pi \times \sqrt{\frac{100}{\pi}} = 20\sqrt{\pi} \, \text{cm}. \]