Question

Sebuah balok mempunyai panjang,lebar,dan tinggi dengan perbandingan 7:4:3. Jika balok itu mempunyai luas permukaan 1.952 cm2, maka volume balok adalah .... cm3
a. 5.176
b. 5.276
c. 5.376
d. 5.476

Pakai cara ya...

Answer 1

P:l:t = 7:4:3
p:l:t = 7x:4x:3x

Lp = 1952
2×(pl+pt+lt) = 1952
2×(7x.4x+7x.3x+4x.3x) = 1952
28x^2 + 21x^2 + 12x^2 = 1952:2
61x^2 = 976
x^2 = 976:61
x = √16
x = 4

p = 7x
p = 7.4
p = 28 cm

l = 4x
l = 4.4
l = 16 cm

t = 3x
t = 3.4
t = 12 cm

V = plt
V = 28.16.12
V = 5376 cm3

Answer 2

P = 7a
l = 4a
t = 3a

luas permukaan balok = 2(pl + pt + lt)
1952 = 2[(7a x 4a) + (7a x 3a) + (4a x 3a)]
1952 = 2(28 a^2 + 21 a^2 + 12 a^2)
1952 = 2(61 a^2)
1952 = 122 a^2
a^2 = 16
a = 4

p = 7a = 7(4) = 28
l = 4a = 4(4) = 16
t = 3a = 3(4) = 12

volume = p x l x t
= 28 x 16 x 12
= 5376 cm^3 (C)