Question

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?

Accepted Answer

B. Let original dimensions be $k, 2k, 3k$. Original volume $V = 6k^3$. Increasing each dimension by $100\%$ doubles them to $2k, 4k, 6k$. New volume $V' = 2k 	imes 4k 	imes 6k = 48k^3$. Increase in volume $= V' - V = 48k^3 - 6k^3 = 42k^3 = 7 	imes (6k^3) = 7V$. So volume increases by 7 times the initial volume.

Volume increase in cuboid

Explanation

Practise this under exam conditions