The surface area of a cuboid is 4212m^2. If it's dimensions are in the ratio 4:3:2 then find the volume of the cuboid
Answers
In the above question the ratio of dimensions of cuboid and it's surface area is also given and it's said to find the volume of the cuboid and according to that here is the answer and hope it will help you.
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Answer:
SA of cuboid = 4212m²
The dimension ratio = 4:3:2
= 4x,3x,2x
l= 4x, b=3x, h=2x
SA of cuboid = 4212
2(lh+bh+bl) = 4212
2(4x×2x + 3x×2x + 3x×4x) = 4212
8x² + 6x² + 12x² = 4212/2
26x² = 2106
x² = 2106/26
x² = 81
x = ± 9
So, x cannot be negative
x = 9
l = 4x
= 4×9
= 36m
b = 3x
= 3×9
= 27m
h = 2x
= 2×9
= 18m
Volume of cuboid = lbh
= 36×27×18
= 972×18
= 17496m²
Hence, the volume of cuboid is 17496m²