Question

If the length of a cuboid is doubled, breadth is halved and height remains the same, find the ratio of the volume of the original cuboid to the volume of the new cuboid.

Answer 1

Originally,

Length of cuboid$=l$

Breadth of cuboid$=b$

Height of cuboid$=h$

Volume$=lbh$

Now,

Length of new cuboid $=2l$

Breadth of new cuboid$=\frac{1}{2}b$

Height of new cuboid$=h$

Volume$=2l\times \frac{b}{2}\times h$

Required ratio$=lbh:2l\times \frac{1}{2}b\times h$

$\Rightarrow ratio=\frac{Volumeoforiginalcuboid}{Volumeofnewcuboid}=\frac{lbh}{lbh}=1:1$

$\therefore$ the ratio is $1:1$

Hence, we can see that the volume is the same. No change has occurred.