Perhatikan gambar berikut! Jika luas juring , tentukan: c. panjang .

Pertanyaan

Perhatikan gambar berikut!

Jika luas juring $undefined$ , tentukan:

c. panjang $begin mathsize 14px style CD with overparenthesis on top end style$ .

Pembahasan Soal:

Diketahui bahwa luas juring $undefined$ .
Untuk mencari panjang busur CD, harus mencari luas lingkaran dahulu, dapat digunakan persamaan:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator luas space lingkaran over denominator luas space COD end fraction end cell equals cell fraction numerator angle 1 space lingkaran over denominator angle COD end fraction space end cell row cell fraction numerator πr squared over denominator luas space juring space COD end fraction end cell equals cell fraction numerator 360 degree over denominator angle COD end fraction space end cell row cell fraction numerator πr squared over denominator 40 space cm squared end fraction end cell equals cell fraction numerator 360 degree over denominator 60 degree end fraction end cell row cell fraction numerator πr squared over denominator 40 space cm squared end fraction end cell equals 6 row cell πr squared end cell equals cell 40 space cm squared cross times 6 end cell row cell πr squared end cell equals cell 240 space cm squared space end cell row cell straight r squared end cell equals cell fraction numerator 240 space cm squared over denominator begin display style 22 over 7 end style end fraction end cell row straight r equals cell 8 comma 74 space cm end cell end table end style$

Sehingga jari-jari lingkaran tersebut adalah $begin mathsize 14px style 8 comma 74 space cm end style$ .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator panjang space CD with overparenthesis on top over denominator keliling space lingkaran end fraction end cell equals cell fraction numerator angle COD over denominator angle 1 space lingkaran end fraction end cell row cell fraction numerator panjang space CD with overparenthesis on top over denominator 2 πr end fraction end cell equals cell fraction numerator angle COD over denominator 360 degree end fraction end cell row cell fraction numerator panjang space CD with overparenthesis on top over denominator 2 cross times 3 comma 14 cross times 8 comma 74 end fraction end cell equals cell fraction numerator 60 degree over denominator 360 degree end fraction end cell row cell fraction numerator panjang space CD with overparenthesis on top over denominator 54 comma 89 space cm end fraction end cell equals cell 1 over 6 end cell row cell fraction numerator panjang space CD with overparenthesis on top over denominator 54 comma 89 space cm end fraction end cell equals cell 1 over 6 end cell row cell panjang space CD with overparenthesis on top end cell equals cell fraction numerator 54 comma 89 space cm over denominator 6 end fraction end cell row cell panjang space CD with overparenthesis on top end cell equals cell space 9 comma 15 space cm end cell end table end style$

Jadi, panjang $begin mathsize 14px style CD with overparenthesis on top end style$ adalah $begin mathsize 14px style 9 comma 15 space cm end style$ .

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 Maret 2021

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