Mensuration Practice Question | Cuboid Volume

Question of The Day09-11-2020

If from a rectangular sheet of paper having dimensions 18 cm × 11 cm, a cuboid is formed without wasting any paper. If ratio of the length, breadth and height of the cuboid is 1 : 2 : 3 respectively, then what will be the volume (in cm3) of the cuboid?

Answer

Correct Answer : d ) 162

Explanation :

Ratio of the length (l), breadth (b) and height (h) of the cuboid is 1 : 2 : 3 respectively

Let us assume length, breadth and height of cuboid be x, 2x and 3x respectively

As, no paper is wasted in making the cuboid

So, Area of rectangular sheet = Total surface area of cuboid

⇒18 * 11 = 2 (lb + bh + hl)

⇒ 18 * 11 = 2 (x * 2x + 2x * 3x + 3x * x)

⇒ 2 (2x² + 6x² + 3x²) = 11 * 18

⇒22x²=18*11

⇒ x = 3

Now,

Volume of cuboid = l * b * h

⇒ Volume = x * 2x * 3x = 6x³ = 6 * (3)³ = 162 cm³

Hence, (d) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc.

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