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Pertanyaan

Gambar di atas adalah menunjukkan bandul jam yang terdiri dari bola dan kerucut. Jika diameter bola begin mathsize 14px style 7 space cm end style dan tinggi kerucut begin mathsize 14px style 12 comma 5 space cm end style.

Hitunglah:

Luas permukaan bandul jam

Volume bandul jam

  1. ...space 

  2. ...space 

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Diketahui:

Diameter atau begin mathsize 14px style straight d equals 7 space cm end style 

Jari-jari atau begin mathsize 14px style straight r equals straight d divided by 2 equals 7 space cm divided by 2 equals 3 comma 5 space cm end style

Tinggi kerucut begin mathsize 14px style straight t equals 12 comma 5 space cm end style 

Nilai begin mathsize 14px style straight pi equals 22 over 7 end style 

Perhatikan gambar, yang diambil sebagai luas permukaan bandul adalah luas selimut kerucut dan luas separuh selimut bola. Bagian alas kerucut menempel pada bagian setengah lingkaran dari bola, berada di dalam. Jadi tidak perlu dihitung.

Tentukan terlebih dahulu garis pelukis kerucut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight s equals cell square root of straight t squared plus straight r squared end root end cell row blank equals cell square root of 12 comma 5 squared plus 3 comma 5 squared end root end cell row blank equals cell square root of 156 comma 25 plus 12 comma 25 end root end cell row blank equals cell square root of 168 comma 5 end root end cell row blank almost equal to 13 end table end style

  • Luas selimut kerucut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell LS space kerucut end cell equals cell straight pi cross times straight r cross times straight s end cell row blank equals cell 22 over 7 cross times 3 comma 5 cross times 13 end cell row blank equals cell fraction numerator 1.001 over denominator 7 end fraction end cell row blank equals cell 143 space cm squared end cell end table end style

  • Luas permukaan setengah bola

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell LP space setengah space bola end cell equals cell 1 half open parentheses 4 cross times straight pi cross times straight r squared close parentheses end cell row blank equals cell 1 half open parentheses 4 cross times 22 over 7 cross times open parentheses 3 comma 5 close parentheses squared close parentheses end cell row blank equals cell 1 half open parentheses fraction numerator 1.078 over denominator 7 end fraction close parentheses end cell row blank equals cell fraction numerator 1.078 over denominator 14 end fraction end cell row blank equals cell 77 space cm squared end cell end table end style

Luas permukaan bandul adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell LP space bandul end cell equals cell LS space kerucut plus LP space setengah space bola end cell row blank equals cell 143 space cm squared plus 77 space cm squared end cell row blank equals cell 220 space cm squared end cell end table end style

  • Volume kerucut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight V. space kerucut end cell equals cell 1 third cross times straight pi cross times straight r squared cross times straight t end cell row blank equals cell 1 third cross times 22 over 7 cross times open parentheses 3 comma 5 close parentheses squared cross times 12 comma 5 end cell row blank equals cell 22 over 21 cross times 12 comma 25 cross times 12 comma 5 end cell row blank equals cell fraction numerator 3.368 comma 75 over denominator 21 end fraction end cell row blank equals cell 160 comma 4 space cm cubed end cell end table end style

  • Volume setengah bola

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight V. space bola end cell equals cell 1 half open parentheses 4 over 3 cross times straight pi cross times straight r cubed close parentheses end cell row blank equals cell 1 half open parentheses 4 over 3 cross times 22 over 7 cross times open parentheses 3.5 close parentheses cubed close parentheses end cell row blank equals cell 1 half open parentheses 88 over 21 cross times 42 comma 875 close parentheses end cell row blank equals cell 1 half open parentheses fraction numerator 3.773 over denominator 21 end fraction close parentheses end cell row blank equals cell fraction numerator 3.773 over denominator 42 end fraction end cell row blank equals cell 89 comma 8 space cm cubed end cell end table end style

Volume bandul adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight V. space bandul end cell equals cell straight V. space kerucut plus straight V. space bola end cell row blank equals cell 160 comma 4 space cm cubed plus 89 comma 8 space cm cubed end cell row blank equals cell 250 comma 3 space cm cubed end cell end table end style

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Pertanyaan serupa

Untuk soal 7 perhatikan tabel di bawah ini. Tentukan luas permukaan dan volume tiap-tiap bangun.

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