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Luas juring POQ=12,56 cm2. Jika panjang jari-jari lingkaran dengan pusat O adalah 8 cm, tentukan panjang busur PQ!

Pertanyaan

Luas juring begin mathsize 14px style POQ equals 12 comma 56 space cm squared end style. Jika panjang jari-jari lingkaran dengan pusat O adalah begin mathsize 14px style 8 space cm end style, tentukan panjang busur PQ!

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

dapat ditentukan panjang busur PQ adalah begin mathsize 14px style 3 comma 14 space cm end style.

Pembahasan

Ingat bahwa, rumus luas juring lingkaran adalah begin mathsize 14px style straight L subscript juring equals fraction numerator straight alpha over denominator 360 degree end fraction cross times straight pi cross times straight r squared end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript juring space POQ end subscript end cell equals cell fraction numerator angle POQ over denominator 360 degree end fraction cross times straight pi cross times straight r squared end cell row cell 12 comma 56 space cm squared end cell equals cell fraction numerator angle POQ over denominator 360 degree end fraction cross times 314 over 100 cross times left parenthesis 8 space cm right parenthesis squared space end cell row cell 12 comma 56 space cm squared end cell equals cell fraction numerator angle POQ cross times 314 cross times 64 space cm squared over denominator 360 degree cross times 100 end fraction end cell row cell 1.256 space cm squared cross times 360 degree end cell equals cell angle POQ cross times 20.096 space cm squared end cell row cell fraction numerator 1.256 space cm squared cross times 360 degree over denominator 20.096 space cm squared end fraction end cell equals cell angle POQ end cell row cell angle POQ end cell equals cell fraction numerator 452.160 degree over denominator 20.096 end fraction end cell row blank equals cell 22 comma 5 degree end cell end table end style

Ingat panjang busur memiliki rumus begin mathsize 14px style fraction numerator straight alpha over denominator 360 degree end fraction cross times 2 cross times straight pi cross times straight r end style, maka panjang busur PQ adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Panjang space busur space PQ end cell equals cell fraction numerator angle POQ over denominator 360 degree end fraction cross times 2 cross times straight pi cross times straight r end cell row blank equals cell fraction numerator 22 comma 5 degree over denominator 360 degree end fraction cross times 2 cross times 314 over 100 cross times 8 space cm end cell row blank equals cell fraction numerator 22 comma 5 degree cross times 5.024 space cm over denominator 360 degree cross times 100 end fraction end cell row blank equals cell fraction numerator 113.040 space cm over denominator 36.000 end fraction end cell row blank equals cell 3 comma 14 space cm end cell end table end style

Jadi, dapat ditentukan panjang busur PQ adalah begin mathsize 14px style 3 comma 14 space cm end style.

188

5.0 (2 rating)

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