Question

If the area of a circle is equal to the area of a square with side \(2 \sqrt{\pi}\) units, what is the diameter of the circle?

• A. 1 unit
• B. 2 units
• C. 4 units
• D. 8 units

Hint:

Recall the formulae for area of circle and square and equate them carefully. Also, simplify roots and powers stepwise.

Answer 1

The Correct Option is C

Step 1: Calculate the area of the square.
Given side of square = \(2 \sqrt{\pi}\) units
Area of square = side \(\times\) side = \((2 \sqrt{\pi})^2 = 4 \times \pi = 4\pi\) square units.
Step 2: Let the radius of the circle be \(r\).
Area of circle = \(\pi r^2\).
Step 3: Since the area of the circle equals the area of the square,
\[ \pi r^2 = 4\pi \] Divide both sides by \(\pi\),
\[ r^2 = 4 \] Therefore,
\[ r = 2 \] Step 4: Diameter of the circle = \(2r = 2 \times 2 = 4\) units.
Hence, the diameter of the circle is 4 units.