Question

The area of a circle is \(49\pi\) square cm. Then its diameter is

• A. 7 cm
• B. 14 cm
• C. 49 cm
• D. 21 cm

Hint:

The area of a circle is proportional to the square of its radius. Use this formula to solve for radius and then the diameter.

Answer 1

The Correct Option is B

Step 1: The formula for the area of a circle is: \[ A = \pi r^2 \] Step 2: Given the area is \(49\pi\), we have: \[ \pi r^2 = 49\pi \] Step 3: Cancel out \( \pi \) from both sides: \[ r^2 = 49 \] Step 4: Taking the square root of both sides: \[ r = 7 \, \text{cm} \] Step 5: The diameter is twice the radius: \[ \text{Diameter} = 2r = 2 \times 7 = 14 \, \text{cm} \] Thus, the correct answer is \( \boxed{14 \, \text{cm}} \).