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Benda pada gambar di samping terbentuk dari gabungan kerucut, tabung, dan setengah bola. Benda tersebut memiliki alas yang sama yaitu berupa lingkaran berjari-jari r. Tinggi kerucut = t subscript K, panjang garis pelukis kerucut = s subscript K dan tinggi tabung = t subscript B. Tentukan rumus luas dan volume bangun di samping. 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

 rumus bangun tersebut memiliki luas bold L subscript bold p table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses pi r s subscript k close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 pi r t subscript B close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 pi r squared close parentheses end cell end table dan volume bold V table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses pi r squared t subscript b close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 over 3 pi r cubed close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 1 third pi r squared t subscript k close parentheses end cell end table.

Pembahasan

Jawaban yang benar dari pertanyaan tersebut adalah bold V table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses pi r squared t subscript b close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end tabletable attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 2 over 3 straight pi r cubed right parenthesis plus open parentheses 1 third straight pi r squared t subscript k close parentheses end cell end table dan  bold L subscript bold p table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses pi r s subscript k close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 pi r t subscript B close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 pi r squared close parentheses end cell end table.

Volume bangun tersebut adalah:

table attributes columnalign right center left columnspacing 0px end attributes row straight V equals cell straight V subscript tabung plus straight V subscript 1 half bola end subscript plus straight V subscript kerucut end cell row blank equals cell open parentheses straight pi r squared t subscript B close parentheses plus open parentheses 1 half cross times 4 over 3 straight pi r cubed close parentheses plus open parentheses 1 third straight pi r squared t subscript k close parentheses end cell row blank equals cell open parentheses straight pi r squared t subscript B close parentheses plus open parentheses 2 over 3 straight pi r cubed close parentheses plus open parentheses 1 third straight pi r squared t subscript k close parentheses end cell end table

Luas permukaan bangun tersebut adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript straight p end cell equals cell straight L subscript selimut space kerucut end subscript plus straight L subscript selimut space tabung end subscript plus straight L subscript 1 half bola end subscript end cell row blank equals cell open parentheses straight pi r s subscript k close parentheses plus open parentheses 2 straight pi r t subscript B close parentheses plus open parentheses 2 straight pi r squared close parentheses end cell end table

Dengan demikian, rumus bangun tersebut memiliki luas bold L subscript bold p table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses pi r s subscript k close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 pi r t subscript B close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 pi r squared close parentheses end cell end table dan volume bold V table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses pi r squared t subscript b close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 over 3 pi r cubed close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 1 third pi r squared t subscript k close parentheses end cell end table.

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