Question

The dimension of cuboid is 4: 3: 2if tsa of cuboid is4212 m^2find volume

Answer 1

Step by step :-

We have :

Here ratio of dimension is 4:3:2 .

Total surface area = 4212 m^2 .

Find sides :-

We know that total surface area of cuboid = 2(lb+bh+hl)

$2(lb + bh + hl) = 4212 \\ 2(4x \times 3x + 3x \times 2x + 2x \times 4x) = 4212 \\ 2(12x + 6x + 8x) = 4212 \\ 2(26x) = 4212 \\ 52x = 4212 \\ x = \frac{4212}{52} \\ x =81m \\ \\ \\ \\ \\ 4x = 324m \\ \\ 3x = 243m \\ \\ 2x = 162 \: m$

We get

$l = 324m \\ \\ b = 243m \\ \\ h = 162m$

Find volume :-

$= l \times b \times h \\ = 324 \times 243 \times 162 \\ = 12754584 {cm}^{3}$

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