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Diketahui luas alas suatu tabung tanpa tutup adala...

Diketahui luas alas suatu tabung tanpa tutup adalah begin mathsize 14px style 616 space cm squared end style, sedangkan luas permukaan tabungnya begin mathsize 14px style 3.080 space cm squared end style. Tinggi tabung tersebut adalah ... cm.

  1. ...space 

  2. ...space 

Jawaban:

Diketahui:

Luas permukaan begin mathsize 14px style LP equals 3.080 space cm squared end style 

Luas salah satu alas tabung begin mathsize 14px style straight L. space lingkaran equals 616 space cm squared end style  

Tentukan terlebih dahulu jari-jari tabung menggunakan rumus luas lingkaran seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Luas space lingkaran end cell equals cell straight pi cross times straight r squared end cell row 616 equals cell 22 over 7 cross times straight r squared end cell row cell 22 straight r squared end cell equals cell 616 cross times 7 end cell row cell 22 straight r squared end cell equals cell 4.312 end cell row cell straight r squared end cell equals cell fraction numerator 4.312 over denominator 22 end fraction end cell row cell straight r squared end cell equals 196 row straight r equals cell plus-or-minus square root of 196 end cell row straight r equals cell plus-or-minus 14 end cell row straight r equals cell 14 space cm end cell end table end style

Diperoleh jari-jari tabung atau begin mathsize 14px style straight r equals 14 space cm end style.

Kemudian gunakan rumus luas permukaan tabung untuk mengetahui tinggi tabung seperti berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row LP equals cell open parentheses 2 cross times straight pi cross times straight r squared close parentheses plus open parentheses 2 cross times straight pi cross times straight r cross times straight t close parentheses end cell row cell 3.080 end cell equals cell 2 cross times straight pi cross times straight r cross times open parentheses straight r plus straight t close parentheses end cell row cell 3.080 end cell equals cell 2 cross times 22 over 7 cross times 14 cross times open parentheses 14 plus straight t close parentheses end cell row cell 3.080 end cell equals cell 616 over 7 cross times open parentheses 14 plus straight t close parentheses end cell row cell 3.080 cross times 7 end cell equals cell 616 cross times open parentheses 14 plus straight t close parentheses end cell row cell 21.560 end cell equals cell 8.624 cross times 616 straight t end cell row cell 616 straight t end cell equals cell 21.560 minus 8.624 end cell row cell 616 straight t end cell equals cell 12.936 end cell row straight t equals cell fraction numerator 12.936 over denominator 616 end fraction end cell row straight t equals cell 21 space cm end cell end table end style

Maka, tinggi tabung tersebut adalah begin mathsize 14px style 21 space cm end style.

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