What will happen to the volume of a cuboid if its: (a) Length is doubled, height is same and breadth is halved? (b) Length is doubled, height is doubled and breadth is same?

Explanation

(a) Given: Length`(l)` is doubled, height`(h)` is same and breadth`(b)` is halved.
Initial dimensions of the cuboid is `l`, `b` and `h`.
Initial volume of the cuboid is `l\timesbtimesh`
Now, of the length`(l)` is doubled and breadth`(b)` is halved:
New dimensions of the cuboid is `2l`, `1/2b` and `h`.
New volume of the cuboid`=2l\times1/2btimesh=l\timesbtimesh`
Hence, the new volume`=`the initial volume.

(b) Given: Length is doubled, height is doubled and breadth is same.
Initial dimensions of the cuboid is `l`, `b` and `h`.
Initial volume of the cuboid is `l\timesbtimesh`
Now, the length`(l)` is doubled and height`(h)` is doubled:
New dimensions of the cuboid is `2l`, `2h` and `b`.
New volume of the cuboid`=2l\timesbtimes2h=4timesl\timesbtimesh=4times`Volume of initial cuboid
Hence, the volume of the new cuboid becomes `4` times the volume of the initial cuboid.