Question

What will be the area of the circle whose diameter is the diagonal of the square whose side is equal to the diagonal of the rectangle whose dimensions are √24 cm and 12 cm?
1. 156 cm square
2. 225 cm square
3. 264 cm square
4. 506 cm square

Answer 1

Correct Answer - Option 3 : 264 cm square

Given:

The diameter of circle is the diagonal of square whose side is equal to the diagonal of rectangle whose dimension is √24 cm and 12 cm

Formula Used:

Diagonal of rectangle = √(l)² + (b)²

Diagonal of square = √2 × side

Area of circle = πr²

Calculation:

The diagonal of rectangle whose length and breadth is √24 cm and 12 cm

⇒ Diagonal = √(√24)² + (12)² = 2√42 cm

Now, the diagonal of rectangle = side of square

⇒ Diagonal of square = √2 × 2√42 = 4√21 cm

Now the diagonal of square = diameter of circle

⇒ Diameter of circle = (4√21)/2 = 2√21 cm

⇒ Area of circle = π × (2√21)² = 264 cm square

∴ The area of circle is 264 cm square.