Question

If the area of a circle is numerically equals to the perimeter of a square with side 11 units, what is the diameter of the circle?
1. 2√14 units 
2. √14 units
3. 2√15 units
4. √17 units

Answer 1

Correct Answer - Option 1 : 2√14 units 

Given

Area of circle = Perimeter of square

Formula used

Area of circle = πr²

Where r is radius

Perimeter of square = 4 × Side

Calculation 

πr² = 4 × 11

⇒ (22/7) × r² = 44

⇒ r² = (44 × 7)/22

⇒ r = √14

Diameter = 2√14 units

∴ Diameter of circle us 2√14 units