Question

The ratio of the length : breadth : height of a cuboid is 5 : 4: 3, and the volume is 7500. what will be its surface area

Answer 1

Let x be the common multiple
length-5x
breadth-4x
height-3x
$7500 = 5x \times 4x \times 3x \\ 60 {x}^{3} = 7500 \\ {x}^{3} = 125 \\ x = 5$
length - 25
breadth- 20
height - 15
surface area
$2(lb + bh + lh) \\ 2(25 \times 20 + 20 \times 15 + 15 \times 25) \\ 2(500 + 300 + 375) \\ 2(1175) \\ 2350 \: {unit}^{2}$
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