Question 54

The length breadth and height of a cuboid are in the ratio 4 : 3 : 2. If the volume of cuboid is 1536 cm, then what will be the total surface area of the cuboid?

Solution

Let length breadth and height of the cuboid are $$4x,3x,2x$$ cm respectively.

Volume of cuboid = $$lbh$$

=> $$4x\times3x\times2x=1536$$

=> $$x^3=\frac{1536}{24}=64$$

=> $$x=\sqrt[3]{64}=4$$

Thus, sides are = 16, 12 and 8 cm

$$\therefore$$ Total surface area of cuboid = $$2(lb+bh+l)$$

= $$2[(16\times12)+(12\times8)+(8\times16)]$$

= $$2\times(192+96+128)$$

= $$2\times416=832$$ $$cm^2$$

=> Ans - (D)

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