Question

The length and breadth and height of a cuboid are ratio 6 ratio 5 ratio 3 if it's total surface area is 504 cm square find its dimensions also find the volume of the cuboid​

Answer 1

Given:

Let length of the cuboid = 6x

Breadth of the cuboid = 5x

Height of the cuboid = 3x

Solution:

Total surface area of the given cuboid = 2 (I x b + b x h + h x l)

= 2(6x x 5x + 5x x 3x + 3x x 6x)

= 2(30×2 + 15×2 + 18×2)

= 2 x 63×2

= 126x²

But we are given total surface area of the given cuboid = 504 cm²

$x^{2} = \frac{504}{126}\\x^{2} = 4\\x = squareroot 4\\x = 2 cm$

Length of the cuboid = 6x = 6 x 2 = 12 cm

Breadth of the cuboid = 5x = 5 x 2 = 10cm

Height of the cuboid = 3x = 3 x 2 = 6 cm

Volume of the cuboid = l x b x h = 12 x 10 x 6 = 720 cm³

Step-by-step explanation:

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