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Volume increase in cuboid

CMAT 2019 · Quantitative Techniques & Data Interpretation · Easy · Mensuration

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The length, breadth and height of a rectangular cuboid are in the ratio 1:2:31 : 2 : 3. If the length, breadth and height are increased by 100%100\% each then what would be the increase in the volume of the cuboid?

  1. A.

    3 times

  2. B.

    7 times

  3. C.

    10 times

  4. D.

    9 times

Answer

B

Explanation

Let original dimensions be k,2k,3kk, 2k, 3k. Original volume V=6k3V = 6k^3. Increasing each dimension by 100%100\% doubles them to 2k,4k,6k2k, 4k, 6k. New volume V′=2k×4k×6k=48k3V' = 2k \times 4k \times 6k = 48k^3.

Increase in volume =V′−V=48k3−6k3=42k3=7×(6k3)=7V= V' - V = 48k^3 - 6k^3 = 42k^3 = 7 \times (6k^3) = 7V. So volume increases by 7 times the initial volume.

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