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Tentukan volume gambar berikut!

Pertanyaan

Tentukan volume gambar berikut!

 

Pembahasan Soal:

Gambar di atas terdiri dari 3 bangun ruang yaitu : kerucut, tabung, dan setengah bola dengan keterangan sebagai berikut :

table attributes columnalign right center left columnspacing 2px end attributes row straight s equals cell 13 space cm end cell row cell straight t space tabung end cell equals cell 12 space cm end cell row straight d equals cell 10 space cm end cell end table 

Langkah 1 : menentukan jari-jari lingkaran

table attributes columnalign right center left columnspacing 2px end attributes row straight r equals cell straight d over 2 end cell row blank equals cell 10 over 2 end cell row blank equals cell 5 space cm end cell end table 

Langkah 2: menentukan tinggi kerucut

table attributes columnalign right center left columnspacing 2px end attributes row cell straight t space kerucut end cell equals cell square root of straight s squared minus straight r squared end root end cell row blank equals cell square root of 13 squared minus 5 squared end root end cell row blank equals cell square root of 169 minus 25 end root end cell row blank equals cell square root of 144 end cell row blank equals cell 12 space cm end cell end table 

Langkah 3 : menentukan volume kerucut 

table attributes columnalign right center left columnspacing 2px end attributes row cell straight V subscript 1 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 3 comma 14 cross times 5 squared cross times 12 end cell row blank equals cell 314 space cm cubed end cell end table 

Langkah 4: menentukan volume tabung

table attributes columnalign right center left columnspacing 2px end attributes row cell straight V subscript 2 end cell equals cell straight pi cross times straight r squared cross times straight t end cell row blank equals cell 3 comma 14 cross times 5 squared cross times 12 end cell row blank equals cell 942 space cm cubed end cell end table 

Langkah 5: menentukan volume setengah bola

table attributes columnalign right center left columnspacing 2px end attributes row cell straight V subscript 3 end cell equals cell 1 half cross times straight V. bola end cell row blank equals cell 1 half cross times 4 over 3 cross times straight pi cross times straight r cubed end cell row blank equals cell 4 over 6 cross times 3 comma 14 cross times 5 cubed end cell row blank equals cell 261 comma 67 space cm cubed end cell end table 

Langkah 6. menentukan volume gabungan 

table attributes columnalign right center left columnspacing 2px end attributes row cell straight V space gab end cell equals cell straight V subscript 1 plus straight V subscript 2 plus straight V subscript 3 end cell row blank equals cell 314 plus 942 plus 261 comma 67 end cell row blank equals cell 1.517 comma 67 space cm cubed end cell end table 

Jadi, volume gambar di atas adalah 1.517 comma 67 space cm cubed  

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 11 Juni 2021

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