The total surface area of a cuboid is 63200 $c m^{2}$ and its length, breadth and height are in the ratio 8:5:3. Find the dimension of the cuboid.

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Solution

length = $8 x$

breadth = $5 x$

height = $3 x$

Total surface area $= 2 (l b + b h + l h) = 63200$

$= 2 (8 x \times 5 x + 5 x \times 3 x + 8 x \times 3 x) = 63200$

$= 2 (40 x^{2} + 15 x^{2} + 24 x^{2}) = 63200$

$= 2 \times 79 x^{2} = 63200$

$= 158 x^{2} = 63200$

$x^{2} = \frac{63200}{158} = 400$

$x = 20 c m$

dimension are length $= 20 \times 8 = 160 c m$

breadth $= 20 \times 5 = 100 c m$

height $= 20 \times 3 = 60 c m$

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