Perbandingan panjang,lebar,dan tinggi balok adalah 5 : 3 : 2 jika luas permukaan balok 558 cm^ maka .... Question from @adla13

October 2018 2 14 Report

Perbandingan panjang,lebar,dan tinggi balok adalah 5 : 3 : 2 jika luas permukaan balok 558 cm^ maka volume balok adalah...

MicoArrafi Cari bilangan pengali :
$$\begin{align} L_{balok}&=2(pl+pt+lt)\\558\ cm^2&=2(5a\times3a+5a\times2a+3a\times2a)\\\frac{558\ cm^2}{2}&=15a^2+10a^2+6a^2\\279\ cm^2&=31a^2\\a&=\sqrt{279\ cm^2:31}\\a&=\sqrt{9\ cm^2}\\a&=3\ cm \end$

Sehingga, volume balok :
$$\begin{align} V_{balok}&=p\times l\times t\\&=5a\times3a\times2a\\&=30a^3\\&=30\times(3\ cm)^3\\&=30\times27\ cm^3\\&=\boxed{810\ cm^3} \end$

2 votes Thanks 2

agatha58 Diket :
p:l:t = 5x:3x:2x
lp = 558 cm^2
ditanya :
v : ?
jawab :
lp = 2( p.l + p.t + l.t)
558 = 2(5x.3x + 5x.2x + 3x.2x)
558 = 2(15×^2+10x^2+6x^2)
558 = 2(31x^2)
558 = 62x^2
558/62 = x^2
9 = x^2
√9 = x
3 = x
p = 5x = 5.3 =15
l = 3x = 3.3 = 9
t = 2x = 2.3 = 6
volume = p.l.t
= 15.9.6
= 810 cm^3

3 votes Thanks 1

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