Question

A square is inscribed in the circle. If the diagonal of square is equal to diameter of circle and area of square is 72 cm² then find the area of circle.
1. 36π cm²
2. 48π cm²
3. 45π cm²
4. None of these 

Answer 1

Correct Answer - Option 1 : 36π cm²

Given 

Area of square = 72 cm²

Formula Used 

Area of square = side²

Area of circle = πR²

Calculation 

Area of square = side²

⇒ side = √72 = 6√2 cm 

Diagonal of square = side√2

⇒ 6√2 × √2 = 12 cm 

Radius of circle = diagonal/2

⇒ 12/2 = 6 cm 

Area of circle = π(6)² 

⇒ 36π cm²

∴ The area of circle is 36π cm²