Question

Площадь кругового  сектора равна 16П см², а радиус окружности 8 см. Найдите длину хорды, стягивающей дугу  этого сектора и площадь получившегося сегмента. ПОМОГИТЕ ПОЖАЛУЙСТА ✅✅✅​

Answer 1

Given :- The area of the circular sector is 16π cm², and the radius of the circle is 8 cm. Find the length of the chord that contracts the arc of this sector and the area of the resulting segment ?

Answer :-

let central angle of the sector is θ .

so,

→ Area of sector = 16 cm² .

→ (θ/360°) * π * r² = 16π

→ (θ/360°) * π * 8² = 16π

→ (θ/360°) * 64π = 16π

→ (θ/360°) = 16π/64π

→ (θ/360°) = (1/4)

→ θ = 90° .

then,

→ Length of chord will be = √(r² + r²) { by pythagoras theorem}

therefore,

→ Length of chord = √(r² + r²) = √(2r²) = √2•r = 8√2 cm (Ans.)

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