Cuboid - complicatef

Three walls of the same cuboid has content 6 cm2, 10 cm2 and 15 cm2. Calculate the volume of the cuboid.

Correct result:

V =  30 cm3

Solution:

ab=6 bc=10 ca=15  c=10/6a a=15/10b b=6/15c  a10/15a=6 a2=6/(10/15) a2=9 a=3  c=10/6a=5 b=6/15c=2   a=3 b=2 c=5 V=abc=30 cm3ab = 6 \ \\ bc= 10 \ \\ ca = 15 \ \\ \ \\ c = 10/6 a \ \\ a = 15/10 b \ \\ b = 6/15 c \ \\ \ \\ a 10/15 a = 6 \ \\ a^2 = 6/ (10/15) \ \\ a^2 = 9 \ \\ a = 3 \ \\ \ \\ c = 10/6 a = 5 \ \\ b = 6/15 c = 2 \ \\ \ \\ \ \\ a = 3 \ \\ b = 2 \ \\ c = 5 \ \\ V = abc = 30 \ \text{cm}^3

a = sqrt(6/(10/15))
c = 10/6 a
b = 6/15 c


a = sqrt(6/(10/15))
c = 10/6•a
b = 6/15•c

15a = 45
10a-6c = 0
15b-6c = 0

a = 3
b = 2
c = 5

Our linear equations calculator calculates it.



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