What will happen to the volume of a cuboid if its:

Solution:

(i) Suppose that the length, breadth and height of the cuboid are $l, b$ and $h$, respectively.

Then, volume $=l \times b \times h$

When its length is doubled, its length becomes $2 \times l$.

When its breadth is halved, its length becomes $\frac{b}{2}$.

The height $h$ remains the same.

Now, volume of the new cuboid $=$ length $\times$ breadth $\times$ height

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

$=l \times b \times h$

$\therefore$ It can be observed that the new volume is the same as the initial volume. So, there is no change in volume.

(ii) Suppose that the length, breadth and height of the cuboid are $l, b$ and $h$, respectively.

Then, volume $=l \times b \times h$

When its length is doubled, its length becomes $2 \times l$.

When its height is double, it becomes $2 \times h$.

The breadth $b$ remains the same.

Now, volume of the new cuboid $=$ length $\times$ breadth $\times$ height

$=2 \times l \times b \times 2 \times h$

$=4 \times l \times b \times h$

$\therefore$ It can be observed that the volume of the new cuboid is four times the initial volume.