Guna has fixed a single door of 3 feet wide in his room whereas Nathan

1.	Guna has fixed a single door of 3 feet wide in his room whereas Nathan has fixed a double door, each 1 1/2 feet wide in his room. From the closed state, if each of the single and double doors can open up to 120°, whose door requires a minimum area?
Answer» (a) Width of the door that Guna fixed = 3 feet. When the door is open the radius of the sector = 3 feet Angle covered = 120° ∴ Area required to open the door = 120°/360° × πr² = 120°/360° × π × 3 × 3 = 37π feet² (b) Width of the double doors that Nathan fixed = 112 feet. Angle described to open = 120° Area required to open = 2 × Area of the sector = 2 × 120°/360° × π × 3/2 × 3/2 feets² = 3π/2 feet² = 12 (3π) feet² ∴ The double door requires the minimum area.

Guna has fixed a single door of 3 feet wide in his room whereas Nathan has fixed a double door, each 1 1/2 feet wide in his room. From the closed state, if each of the single and double doors can open up to 120°, whose door requires a minimum area?

Answer»

(a) Width of the door that Guna fixed = 3 feet.

When the door is open the radius of the sector = 3 feet

Angle covered = 120°

∴ Area required to open the door = 120°/360° × πr²

= 120°/360° × π × 3 × 3

= 37π feet²

(b) Width of the double doors that Nathan fixed = 112 feet.

Angle described to open = 120°

Area required to open = 2 × Area of the sector

= 2 × 120°/360° × π × 3/2 × 3/2 feets² = 3π/2 feet²

= 12 (3π) feet²

∴ The double door requires the minimum area.