Rumus Volume dan Luas Permukaan Bangun Ruang

1. Bangun Ruang Sisi Lengkung

a. Tabung (Silinder )
Dalam tabung (silinder) berlaku rumus-rumus:
i. d = 2r atau r = ½ d
ii. La= Lb= πr 2 = ¼d2
iii. L s= 2πrt = πdt
iv. L p= L a+ Lb + L s= 2πr (r + t) = π d (d + t)
v. V= Lb t = L a t = π r 2 t
tabungdengan:
r = jari-jari atas/alas tabung
d = diameter atas/ alas tabung
t= tinggi tabung
La = luas bidang atas tabung
Lb = luas bidang bawah/ alas/ dasar tabung
Ls = luas selimut/ selubung tabung
Lp= luas permukaan tabung
V = volume/ isi tabung

b. Kerucut
Dalam kerucut berlaku rumus-rumus:
i. d = 2r atau r = ½ d
ii. p2= t 2+ r 2
iii. Lb= πr 2 = ¼πd2
iv. L s= πrp = ½πdp
v. L p= Lb + L s= πr (r + p) =½ πd (d + p)
vi. V = π/3 r 2 t
vii. φ = r/p x 360

kerucutdengan:
r= jari-jari alas kerucut
d= diameter alas kerucut
t = tinggi kerucut
p = panjang garis pelukis atau apotema
Lb = luas bidang bawah/ alas/ dasar kerucut
Ls = luas selimut/ selubung kerucut
Lp = luas permukaan kerucut
V = volume/ isi kerucut
φ = sudut pusat rebahan
c. Kerucut Terpancung
Dalam kerucut terpancung berlaku rumus-rumus:
i. d1 = 2r1 atau r1 = ½ d 1
ii. d2 = 2r2 atau r2 = ½ d 2
iii. Lb= πr 12 = ¼ πd12
iv. La= πr 22 = ¼ πd22
v. L s= πp (r 1+ r 2)= ½πp (d1+ d2)
vi. L p= Lb + La+ L s= πp(r 1+ r 2) + π p(r 12+ r 22)
vii. V = π/3 t (r1 2+ r22 + r 1r2)
kerucutterpancungdengan:
r1 = jari-jari bidang alas/ dasar/ bawah kerucut terpancung
d1 = diameter bidang alas/ dasar/ bawah kerucut terpancung
r2 = jari-jari bidang atas kerucut terpancung
d2 = diameter bidang atas kerucut terpancung
t = tinggi kerucut terpancung
p = panjang garis pelukis atau apotema kerucut terpancung
Lb = luas bidang bawah/ alas/ dasar kerucut terpancung
La = luas bidang atas kerucut terpancung
Ls = luas selimut/ selubung kerucut terpancung
Lp = luas permukaan kerucut terpancung
V = volume/ isi kerucut terpancung

d. Bola
Dalam bola berlaku rumus-rumus:
i. D = 2R atau R= ½ D
ii. d = 2r atau r = ½ d
iii. R2 = h2+ r 2
iv. Lt = 2πRt = πDt
v. L p= 4πR 2= πD2
vi. V = 4π/ 3 R3= π/ 3D3
vii. Vt= πt2 (3R- t)
boladengan:
R = jari-jari bola
D = diameter bola
r = jari-jari bidang lingkaran
d = diameter bidang lingkaran
h = jarak pusat bola ke bidang lingkaran
t = jarak dari pusat bidang lingkaran ke kulit bola
Lp = luas permukaan bola
Lt = luas bidang lengkung tembereng
V = volume/ isi bola
Vt = volume/ isi tembereng bola

2. Bangun Ruang Sisi Datar

a. Kubus
Dalam kubus berlaku rumus:
ds= a √2
dr= a √3
Lp= 6 a 2

V = a^ 3

dengan:
a = panjang rusuk kubus
ds = panjang diagonal sisi kubus
dr = panjang diagonal ruang kubus
Lp = luas permukaan kubus
V = volume/ isi kubus

b. Balok
Dalam balok berlaku rumus-rumus:
d1= √ (p2 + l2)
d2= √ (p2 + t2)
d3= √ (l2 + t2)
dr= √ (p2 + l2+ t2)
Ls= 2 (p + l )t
Lp= 2 (pl + pt + lt)
V = plt
dengan :
p = panjang balok
l = lebar balok
t = tinggi balok
d1 = panjang diagonal sisi alas/ atas
d2 = panjang diagonal sisi depan/ belakang
d3 = panjang diagonal sisi samping kiri/ kanan
dr = panjang diagonal ruang balok
Ls = luas selimut/ selubung balok
Lp = luas permukaan balok
V = volume/ isi balok

c. Prisma Tegak
Dalam prisma tegak berlaku rumus-rumus:
Luas selimut/ selubung prisma tegak = keliling alas x panjang rusuk tegak

Luas permukaan prisma tegak
Luas permukaan prisma tegak =
luas selimut + luas bidang alas + luas bidang atas
= luas selimut + 2 x luas bidang alas
= luas selimut + 2 x luas bidang atas
Volume prisma tegak= luas bidang bawah/ alas/ dasar x panjang rusuk tegak (tinggi)
= luas bidang atas x panjang rusuk tegak (tinggi)

d. Limas (Piramida)
Dalam limas (piramida) berlaku rumus-rumus:
Luas permukaan limas = luas alas + jumlah sisi tegak = luas alas + n x luas sisi tegak
Lp = Lb + n x L
Volume limas = 1/3 luas alas x tinggi
V = 1/3 Lb x t

Rumus Volume dan Luas Permukaan Bangun Ruang, 1.0 out of 5 based on 1 rating

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47 Comments

  1. Ubay Nyzhar

    April 8, 2011 at 3:39 am

    8) 8) 8)

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  2. i like mat..

    April 10, 2011 at 8:23 am

    :-) :!: :evil: :lol: :o

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  3. Ubay Nyzhar

    April 11, 2011 at 8:06 am

    like too 8) 8) 8)

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    Rating: -1 (from 1 vote)
  4. Nugraenie Ntu Qw

    May 3, 2011 at 1:17 pm

    :D :-) :( :o 8O :? 8) :lol: :x :P :oops: :cry: :evil: :twisted: :roll: :wink: :!: :?: :idea: :arrow: :| :mrgreen:

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  5. Abram

    May 4, 2011 at 3:35 am

    :D :-) :( :o 8O :? 8) :lol: :x :P :oops: :cry: :evil: :twisted: :roll: :wink: :!: :?: :idea: :arrow: :| :mrgreen: Aku Suka Ini Menambang ilmu pungetahuan

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    • Anisa

      February 9, 2014 at 10:17 am

      Thanks buat rumus” nya sangat bermanfaat :)

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  6. Ubay Nyzhar

    May 5, 2011 at 2:08 am

    :!: :!: :!:

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    Rating: -1 (from 1 vote)
  7. caesilia

    May 10, 2011 at 1:38 am

    baguss banget,…..menambah wawasan ….blog yg bermanfaat :!: :!: :!:

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  8. Ubay Nyzhar

    May 11, 2011 at 2:45 am

    thingqyu… 8) 8) 8)

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    Rating: -1 (from 1 vote)
  9. Lulu

    May 17, 2011 at 6:34 am

    I Like this….. :!: :!: :lol: 8)

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    Rating: -1 (from 1 vote)
  10. Lulu

    May 17, 2011 at 6:36 am

    its good :) :-) :( :o 8O :? 8) :lol: :lol: :oops: :| :arrow: :idea: :!: :wink: :roll: :cry: :P

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  11. Ubay Nyzhar

    May 19, 2011 at 6:52 am

    tq … :)

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  12. ria

    May 19, 2011 at 9:46 am

    :( :cry: aq pusing..mnta artikel tentang bidang singgung pada tabung dongg….
    pleassseeee….. :?

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  13. Ubay Nyzhar

    May 20, 2011 at 1:05 am

    ok … msh ngrancang sob … 8) :wink:

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    Rating: -1 (from 1 vote)
  14. verdian

    June 6, 2011 at 4:03 am

    ku gk ngerti masih tentang limass……pleaseee,kasih yg lbih lngkap keterangnnya donk :roll:

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  15. rifki

    June 18, 2011 at 11:35 am

    rumus yg buat prisma gg ngerti :( :( :(

    bisa diperjelas gg luas bidang alas dan luas bidang atasnya??? terus Luas permukaan limas juga saya juga kurang ngerti…

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  16. Riza

    July 11, 2011 at 1:31 pm

    :!: :( 8O :P 8O :!: :evil:

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  17. kuntowati

    July 14, 2011 at 9:02 am

    :!: Okey good tambah point ilmu dech… :-)

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  18. sopian saurie

    July 16, 2011 at 5:54 pm

    :!:
    :!:
    :!:

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  19. Rafid

    September 15, 2011 at 1:07 pm

    mats memang asik 8)

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  20. Rafid

    September 15, 2011 at 1:11 pm

    he :-) :( :o 8O :? 8) :lol: :x :P

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  21. beno

    September 19, 2011 at 12:17 pm

    ttetet :D :-) :( :o 8O :? 8) :lol: :x

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  22. dila

    September 20, 2011 at 9:50 am

    adoh.. aku kungang ngarti :x … huaaa :cry:

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  23. bgs skale

    October 11, 2011 at 2:54 am

    :!: :!: :!: :!:

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  24. DOTA NEVER MORE

    October 11, 2011 at 2:57 am

    apik men :!: :x :D :!: :arrow:

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  25. ngah ngoh

    October 11, 2011 at 2:59 am

    wah jos jos jos sekale :wink: :!: :!: :!: :!:

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  26. DOTA NEVER MORE

    October 11, 2011 at 3:01 am

    aku kok bingung yo cak……….. :lol: :x :P :cry:

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  27. dota alstar tinker

    October 11, 2011 at 3:11 am

    :D :-) 8) :mrgreen: edan tenan :!: :wink:

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  28. Erik

    October 11, 2011 at 4:07 pm

    Bs tolong saya dengan soal “taksiran” ini???

    Berapa sentimeter KUBIK dalamnya kepala anda? :roll:

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  29. ICHSAN

    October 12, 2011 at 2:41 pm

    thank you ya. :D :( 8) :lol: :x :twisted: :!: :idea: :arrow: :| :mrgreen: :wink: :o 8O :? :oops: :cry: :P :( 8) :twisted: :x :x :x :x :x :!: :!: :!: :!: :!:

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  30. Faqih

    October 13, 2011 at 1:16 pm

    adug agak bingung :? kurang ngerti nich :cry: tp tetap enjoy 8)

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    • it's me !

      November 5, 2013 at 3:56 pm

      gue juga gak ngerti -_-

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  31. nisaa ul

    October 20, 2011 at 12:55 pm

    good job :lol: :P :!: :!:

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  32. tarjoks

    October 20, 2011 at 8:15 pm

    tq bgt dueh,,,,,,, sangat mmbantu kt2 yg msh bljr nueh :-) :-) :-) :-) :!:

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  33. rasyied

    November 2, 2011 at 8:58 am

    yee ujian matematika pasti lulus

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  34. erlangga

    November 23, 2011 at 12:08 am

    thanks yy rumus’a
    8) :D :twisted: :x :arrow: :mrgreen: :!:

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  35. erlangga

    November 23, 2011 at 12:09 am

    :lol: :x :D :-) :( :o 8O :? 8) :P :oops: :cry: :evil: :twisted: :roll: :wink: :!: :?: :idea: :arrow: :| :mrgreen:

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  36. nanikakina

    December 2, 2011 at 12:45 pm

    :lol: 8) :twisted: :arrow: :| :P

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  37. monic

    December 15, 2011 at 10:45 am

    sangat membantu :lol: :!: :| :evil: :oops: :P :x 8) :D

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  38. audri

    December 23, 2011 at 1:52 pm

    I LIKE IT :o 8O :!: :D 8) :arrow:

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  39. Adrina

    May 29, 2012 at 7:30 am

    Thanks for all^^ i like it

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  40. M.Kharisma Hakim

    September 21, 2012 at 1:58 pm

    Awesome man, thanks for all :)

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  41. richard

    July 11, 2013 at 3:35 am

    apawekepo.
    like tapiii :D :)

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  42. gunawan sitorus

    September 21, 2013 at 3:14 am

    Mkasih bnget blok nya mas brow…
    tpi mnta tlng agar skalian cntoh soal y
    Ok..bos.

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  43. Annisa Amalia

    October 6, 2013 at 3:15 am

    keren… lebih lengkap lagi kalau ada jaring-jaringnya :)

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  44. nitromento

    October 22, 2013 at 4:27 pm

    yo temans, lokasi admin klikbelajar.com di mana, ya? boleh konkow di TKP, gak? ogut ‘setan numerik’ yg ‘belum tentu arah’.. semoga bisa saling tukarpikiran, gitu.. tenkyu temans.. bravo kalkulasi..

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    • Administrator

      Administrator

      October 23, 2013 at 6:53 am

      Halo Mas, bisa kongkow bareng2 di forums aja gmn ??
      sekalian biar rame disini, biar kita bs sharing2 disini sekalian
      Atau mau daftar juga jadi author di klikbelajar ? :)

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