Question 19

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

Solution

Given the length, breadth and height of a rectangular cuboid are in the ratio 1: 2 : 3.

Let the length, breadth and height be k, 2k, and 3k units where 'k' is a constant.

Volume of the cuboid(V') = $$l\times b\times h$$ units = $$k\times 2k\times 3k$$  = $$6k^3$$ units

Given the length, breadth and height are increased by 100% each .

Then the new length, breadth and height will be doubled.

So new length, breadth and height of the rectangular cuboid are 2k, 4k, and 6k units.

New Volume of the cuboid (V') = $$2k\times 4k\times 6k = 48k^3$$ units.

Increase in the volume of the cuboid = V' - V = $$48k^3 - 6k^3 = 42k^3 = 7 [6k^3] = 7V$$

Therefore the volume has increased 7 times the initial volume.

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