Luas sebuah juring 40 cm bila jari – jarinyab10 cm tentukan besar sudut

Pertanyaan:

Luas sebuah juring 40 cm bila jari – jarinyab10 cm tentukan besar sudut

Rumus: Luas lingkaran ( L l i n g k a r a n cap L sub l i n g k a r a n end-sub L l i n g k a r a n ) dihitung menggunakan rumus L = π r 2 cap L equals pi r squared L = π r 2 . Perhitungan: L l i n g k a r a n = π × ( 10 cm ) 2 = 100 π cm 2 cap L sub l i n g k a r a n end-sub equals pi cross open paren 10 space cm close paren squared equals 100 pi space cm squared L l i n g k a r a n = π × ( 1 0 c m ) 2 = 1 0 0 π c m 2

Rumus: Luas juring ( L j u r i n g cap L sub j u r i n g end-sub L j u r i n g ) terkait dengan sudut pusat ( θ theta θ ) dan luas lingkaran melalui rumus: L j u r i n g = θ 360 ∘ × L l i n g k a r a n cap L sub j u r i n g end-sub equals the fraction with numerator theta and denominator 360 raised to the composed with power end-fraction cross cap L sub l i n g k a r a n end-sub L j u r i n g = θ 3 6 0 ∘ × L l i n g k a r a n

Perhitungan: Kita tahu L j u r i n g = 40 cm 2 cap L sub j u r i n g end-sub equals 40 space cm squared L j u r i n g = 4 0 c m 2 dan L l i n g k a r a n = 100 π cm 2 cap L sub l i n g k a r a n end-sub equals 100 pi space cm squared L l i n g k a r a n = 1 0 0 π c m 2 . Kita susun ulang rumus untuk mencari θ theta θ :

θ = L j u r i n g L l i n g k a r a n × 360 ∘ theta equals the fraction with numerator cap L sub j u r i n g end-sub and denominator cap L sub l i n g k a r a n end-sub end-fraction cross 360 raised to the composed with power θ = L j u r i n g L l i n g k a r a n × 3 6 0 ∘ θ = 40 cm 2 100 π cm 2 × 360 ∘ theta equals the fraction with numerator 40 space cm squared and denominator 100 pi space cm squared end-fraction cross 360 raised to the composed with power θ = 4 0 c m 2 1 0 0 π c m 2 × 3 6 0 ∘ θ = 40 100 π × 360 ∘ theta equals the fraction with numerator 40 and denominator 100 pi end-fraction cross 360 raised to the composed with power θ = 4 0 1 0 0 π × 3 6 0 ∘ θ = 4 10 π × 360 ∘ theta equals the fraction with numerator 4 and denominator 10 pi end-fraction cross 360 raised to the composed with power θ = 4 1 0 π × 3 6 0 ∘ θ = 2 5 π × 360 ∘ theta equals the fraction with numerator 2 and denominator 5 pi end-fraction cross 360 raised to the composed with power θ = 2 5 π × 3 6 0 ∘ θ = 720 ∘ 5 π theta equals the fraction with numerator 720 raised to the composed with power and denominator 5 pi end-fraction θ = 7 2 0 ∘ 5 π θ = 144 ∘ π theta equals the fraction with numerator 144 raised to the composed with power and denominator pi end-fraction θ = 1 4 4 ∘ π

Menggunakan nilai π ≈ 3.14 pi is approximately equal to 3.14 π ≈ 3 . 1 4 , nilai perkiraan sudutnya adalah: θ ≈ 144 ∘ 3.14 ≈ 45.86 ∘ theta is approximately equal to the fraction with numerator 144 raised to the composed with power and denominator 3.14 end-fraction is approximately equal to 45.86 raised to the composed with power θ ≈ 1 4 4 ∘ 3 . 1 4 ≈ 4 5 . 8 6 ∘ (Perhitungan Python menghasilkan ∼ 45.84 ∘ tilde 45.84 raised to the composed with power ∼ 4 5 . 8 4 ∘ )

Besar sudut juring tersebut adalah 144 π the fraction with numerator 144 and denominator bold pi end-fraction 1 4 4 π derajat, yang setara dengan kira-kira 45.84 ∘ 45.84 raised to the composed with power 4 5 . 8 4 ∘ .