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Question

A cuboid has edges of x cm, 1cm and 2cm. The total surface area of the cuboid has a numerical value which is some integral multiple of the numerical values of its volume. What is the value of x for minimum possible positive integral multiple ?

A
5cm
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B
2cm
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C
3cm
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D
4cm
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Solution

The correct option is B 2cm
Total surface of the cuboid =2(x+2+2x)
=6x+4
Volume of the cuboid =l×b×h
=x×1×2=2x
Given, 6x+4=n×2x , where n is an ingeger
=>(2n6)x=4
Since x is the length of the cuboid and length cannot be negative,
x(2n6)>0 or 2n>6 or n>3
n is positive integer, minimum value of n=4
=>6x+4=2×4x
=>x=2cm.

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