Roboguru

Perhatikan gambar berikut! Tabung di samping diisi air hingga penuh. Jika diameter dan tinggi tabung sama dengan diameter bola yaitu 60 cm, tentukan volume air yang dapat ditampung oleh tabung!

Pertanyaan

Perhatikan gambar berikut!

Tabung di samping diisi air hingga penuh. Jika diameter dan tinggi tabung sama dengan diameter bola yaitu 60 cm, tentukan volume air yang dapat ditampung oleh tabung!

Pembahasan Soal:

Pada gambar, diketahui tabung yang diisi oleh bola dimana jari-jari tabung dan bola (r) sama yaitu 30 cm. tinggi tabung (t) sama dengan diameter bola yaitu 60 cm. Sehingga,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight V subscript air space end subscript end cell equals cell straight V subscript tabung minus straight V subscript bola end cell row blank equals cell πr squared straight t minus 4 over 3 πr cubed end cell row blank equals cell πr squared open parentheses 2 straight r close parentheses minus 4 over 3 πr cubed end cell row blank equals cell 2 over 3 πr cubed end cell row blank equals cell 2 over 3 open parentheses 3 comma 14 close parentheses open parentheses 30 cubed close parentheses end cell row blank equals cell 56.520 space cm cubed end cell end table end style

Dengan demikian, volume air yang dapat ditampung adalah 56.520 cm3.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

L. Marlina

Mahasiswa/Alumni Institut Teknologi Bandung

Terakhir diupdate 31 Agustus 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Tentukan luas permukaan dan volume bangun ruang gabungan berikut.

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell Luas space tabung space tanpa space atap end cell equals cell italic pi italic r squared plus 2 italic pi italic r italic t end cell row blank equals cell 3 comma 14 cross times 10 squared plus 2 cross times 3 comma 14 cross times 10 cross times 25 end cell row blank equals cell 314 plus 1.570 end cell row blank equals cell 1.884 end cell row blank blank blank row cell Luas space 1 half space bola end cell equals cell 2 italic pi italic r squared end cell row blank equals cell 2 cross times 3 comma 14 cross times 10 squared end cell row blank equals 628 row blank blank blank row cell Luas space gabungan end cell equals cell 1.884 plus 628 end cell row blank equals cell 2.512 space cm squared space end cell row blank blank blank row cell Volume space tabung end cell equals cell italic pi italic r squared italic t end cell row blank equals cell 3 comma 14 cross times 10 squared cross times 25 end cell row blank equals cell 7.850 end cell row blank blank blank row cell Volume space 1 half space bola end cell equals cell 1 half cross times 4 over 3 italic pi italic r cubed end cell row blank equals cell 2 over 3 cross times 3 comma 14 cross times 10 cubed end cell row blank equals cell 2.093 comma 3 end cell row blank blank blank row cell Volume space gabungan end cell equals cell 7.850 plus 2.093 comma 3 end cell row blank equals cell 9.943 comma 3 space cm cubed space end cell end table

0

Roboguru

Perhatikan gambar-gambar di bawah ini. Tentukan volume tiap-tiap bangun.

Pembahasan Soal:

a. Tabung

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight r equals cell 5 space cm end cell row straight t equals cell 14 space cm end cell row straight V equals cell straight pi cross times straight r squared cross times straight t end cell row blank equals cell straight pi cross times 5 squared cross times 14 end cell row blank equals cell 350 straight pi end cell row blank equals cell 350 cross times 22 over 7 end cell row blank equals cell 1.100 cm squared end cell end table end style 

b. Tabung

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight d equals cell 24 space dm end cell row straight t equals cell 40 space dm end cell row straight V equals cell straight pi cross times straight r squared cross times straight t end cell row blank equals cell straight pi cross times 12 squared cross times 40 end cell row blank equals cell 5.760 straight pi end cell row blank equals cell 5.760 cross times 3 comma 14 end cell row blank equals cell 18.086 comma 4 space dm squared end cell end table end style 

c. Tabung

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight r equals cell 1 space straight m end cell row straight t equals cell 2 space straight m end cell row straight V equals cell straight pi cross times straight r squared cross times straight t end cell row blank equals cell straight pi cross times 1 squared cross times 2 end cell row blank equals cell 2 straight pi end cell row blank equals cell 2 cross times 3 comma 14 end cell row blank equals cell 6 comma 28 space straight m squared end cell end table end style 

d. Kerucut

undefined 

mencari undefined 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight r squared end cell equals cell straight s squared minus straight t squared end cell row blank equals cell 15 squared minus 12 squared end cell row blank equals cell 225 minus 144 end cell row blank equals 81 row straight r equals cell 9 space cm end cell end table end style 

mencari Volume

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight V equals cell 1 third cross times straight pi cross times straight r cross times straight r cross times straight t end cell row blank equals cell 1 third cross times straight pi cross times 9 cross times 9 cross times 12 end cell row blank equals cell 324 cross times straight pi end cell row blank equals cell 324 cross times 3 comma 14 end cell row blank equals cell 1.017 comma 36 space cm cubed end cell end table end style 

e. Kerucut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight d equals cell 16 space dm end cell row straight t equals cell 15 space dm end cell row straight V equals cell 1 third cross times straight pi cross times straight r cross times straight r cross times straight t end cell row blank equals cell 1 third cross times straight pi cross times 8 cross times 8 cross times 15 end cell row blank equals cell 320 cross times straight pi end cell row blank equals cell 320 cross times 3 comma 14 end cell row blank equals cell 1.004 comma 8 space dm cubed end cell end table end style 

f. Kerucut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight d equals cell 2 space straight m end cell row straight s equals cell 2 space straight m end cell end table end style 

mencari begin mathsize 11px style straight t end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight t squared end cell equals cell straight s squared minus straight r squared end cell row blank equals cell 2 squared minus 1 squared end cell row blank equals cell 4 minus 1 end cell row blank equals 3 row straight t equals cell √ 3 space straight m end cell end table end style 

mencari Volume

Error converting from MathML to accessible text. 

g. Bola

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight d equals cell 24 space cm end cell row straight r equals cell 12 space cm end cell row straight V equals cell 4 over 3 straight pi cross times straight r cubed end cell row blank equals cell 4 over 3 straight pi cross times 12 cubed end cell row blank equals cell 2.304 straight pi end cell row blank equals cell 7.234 comma 56 space cm cubed end cell end table end style 

h. Bola

Error converting from MathML to accessible text. 

i. Bola

Error converting from MathML to accessible text. 

j. Tabung

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight d equals cell 12 space straight m space end cell row straight h equals cell 15 space straight m end cell end table end style 

mencari undefined 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight t squared end cell equals cell straight h squared minus straight d squared end cell row blank equals cell 15 squared minus 12 squared end cell row blank equals cell 225 plus 144 end cell row blank equals 81 row straight t equals cell 9 space straight m end cell end table end style 

mencari Volume

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight V equals cell straight pi cross times straight r squared cross times straight t end cell row blank equals cell straight pi cross times 6 squared cross times 9 end cell row blank equals cell 324 straight pi end cell row blank equals cell 324 cross times 3 comma 14 end cell row blank equals cell 1.017 comma 36 straight m squared end cell end table end style 

k. Kerucut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight r equals cell 6 space dm end cell row straight t equals cell 9 space dm end cell row straight V equals cell 1 divided by 3 cross times straight pi cross times straight r cross times straight r cross times straight t space end cell row blank equals cell 1 third cross times straight pi cross times 6 cross times 6 cross times 9 end cell row blank equals cell 108 cross times straight pi end cell row blank equals cell 108 cross times 3 comma 14 end cell row blank equals cell 339 comma 12 space dm cubed end cell end table end style 

l. Bola

Error converting from MathML to accessible text.  

0

Roboguru

Untuk soal perhatikan tabel di bawah ini. Kemudian bandingkan jawabanmu dengan rumus bangun-bangun pada sebelah kiri. a. Apakah volume bangun sebelah kanan selalu sama dengan setengah kali volume b...

Pembahasan Soal:

a. Ya, volume bangun sebelah kanan akan selalu sama dengan setengah volume bangun sebelah kiri


b. Untuk volume bangun ruang, volume bangun yang tak utuh (sebagian) akan sama dengan hasil kali dari besar bagian bangun dengan volume asal bangun ( volume utuh ). Dalam kasus ini                adalah  undefined  

0

Roboguru

Diameter tabung di atas adalah 28 cm dengan tinggi tabung 10 cm. Jika tinggi bangun gabungannya 25 cm, maka volume bangun tersebut adalah ... cm3.

Pembahasan Soal:

Diketahui:

Tabung

diameter = 28 cm

jari - jari = 14 cm

tinggi = 10 cm

Kerucut

diameter = 28 cm

jari - jari = 14 cm

tinggi = 25 -10 =15 cm

Ditanya:

Volume bangun = ?

Jawab:

Volume tabung = straight pi times straight r squared times straight t 

Volume kerucut = 1 third times straight pi times straight r squared times straight t 

Volume bangun 

equals Volume space tabung plus volume space kerucut equals straight pi times straight r squared times straight t plus 1 third times straight pi times straight r squared times straight t equals 22 over 7 times 14 squared times 10 plus 1 third times 22 over 7 times 14 squared times 15 equals 6.160 plus 3.080 equals 9.240

Jadi, volume bangun tersebut adalah 9.240 cm3.

0

Roboguru

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

Pembahasan Soal:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a. space Luas space Permukaan end cell equals cell luas space alas space tabung plus luas space selimut space tabung plus luas space selimut space kerucut end cell row blank equals cell pi r squared plus 2 pi r t plus pi r s end cell row blank equals cell pi r left parenthesis r plus 2 t plus s right parenthesis end cell end table end style      

            Untuk mendapatkan nilai begin mathsize 14px style s end style atau garis pelukis digunakan konsep phytagoras pada kerucut sebagai berikut: 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell s squared end cell equals cell t squared plus r squared end cell row s equals cell square root of t squared plus r squared end root end cell end table end style  

     begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row volume equals cell volume space tabung plus volume space kerucut end cell row blank equals cell pi r to the power of 2 space end exponent t space plus 1 third pi r squared t end cell row blank equals cell 4 over 3 pi r squared t end cell end table end style  

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight b. space Luas space permukaan end cell equals cell 2 cross times space luas space selimut space kerucut space plus luas space selimut space tabung end cell row blank equals cell 2 cross times pi r s plus 2 pi r t end cell row blank equals cell 2 pi r s plus 2 pi r t end cell row blank equals cell 2 pi r open parentheses s plus t close parentheses end cell end table end style 

 

    begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row Volume equals cell 2 cross times volume space kerucut plus volume space tabung end cell row blank equals cell 2 cross times 1 third pi r squared t plus pi r squared t end cell row blank equals cell 2 over 3 pi r squared t plus pi r squared t space end cell row blank equals cell left parenthesis 2 over 3 plus 1 right parenthesis pi r squared t end cell row blank equals cell 5 over 3 pi r squared t end cell end table end style  

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight c. space Luas space permukaan end cell equals cell 1 half luas space permukaan space bola space plus space luas space selimut space kerucut end cell row blank equals cell 1 half cross times 4 pi r squared plus pi r s end cell row blank equals cell 2 pi r squared plus pi r s end cell row blank equals cell pi r open parentheses 2 r plus s close parentheses end cell end table end style 

 

     begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row Volume equals cell 1 half volume space bola plus volume space kerucut end cell row blank equals cell 1 half cross times 4 over 3 pi r cubed plus 1 third pi r squared t end cell row blank equals cell 2 over 3 pi r cubed plus 1 third pi r squared t end cell row blank equals cell 1 third pi r squared left parenthesis 2 r plus t right parenthesis end cell end table end style   

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell d. Luas space Permukaan end cell equals cell 1 half Luas space permukaan space bola plus luas space selimut space tabung plus luas space tutup space tabung end cell row blank equals cell 1 half cross times 4 pi r squared plus 2 pi r t plus pi r squared end cell row blank equals cell 2 pi r squared plus 2 pi r t plus pi r squared end cell row blank equals cell 3 pi r squared plus 2 pi r t end cell row blank equals cell pi r open parentheses 3 r plus 2 t close parentheses end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Volume space end cell equals cell 1 half Volume space bola plus volume space tabung end cell row blank equals cell 1 half cross times 4 over 3 pi r cubed plus pi r squared t end cell row blank equals cell 2 over 3 pi r cubed plus pi r squared t end cell row blank equals cell pi r squared open parentheses 2 over 3 r plus t close parentheses end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight e. space Luas space Permukaan space end cell equals cell 1 half space luas space permukaan space bola space plus space luas space selimut space tabung space plus luas space selimut space kerucut end cell row blank equals cell 1 half cross times 4 pi r squared plus 2 pi r t plus pi r s end cell row blank equals cell 2 pi r squared plus 2 pi r t plus pi r s end cell row blank equals cell pi r open parentheses 2 r plus 2 t plus s close parentheses end cell end table end style 

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row Volume equals cell 1 half volume space bola plus volume space tabung plus volume space kerucut end cell row blank equals cell 1 half cross times 4 over 3 pi r cubed plus pi r squared t plus 1 third pi r squared t end cell row blank equals cell 2 over 3 pi r cubed plus pi r squared t plus 1 third pi r squared t end cell row blank equals cell pi r squared left parenthesis 2 over 3 r plus 4 over 3 t right parenthesis end cell row blank equals cell 2 over 3 pi r squared left parenthesis r plus 2 t right parenthesis end cell end table end style   

 

undefined 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row volume equals cell 2 cross times 1 half volume space bola plus volume space tabung end cell row blank equals cell 4 over 3 pi r cubed plus pi r squared t end cell row blank equals cell pi r squared open parentheses 4 over 3 r plus t close parentheses end cell end table end style

 

 

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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