Question

Obtain the volume of a rectangular box with the given length, breadth, and height respectively.
$2\text{p}$, $4\text{q}$, $8\text{r}$.
(a) $4\text{pqr}$
(b) $64\text{pqr}$
(c) $6\text{pr}$
(d) $4\text{pq}$

Answer 1

Hint: A rectangular box is a cuboid. We will use the formula for the volume of a cuboid. The volume of a cuboid is given by $V=l\times b\times h$ where $l$ is the length, $b$ is the breadth, and $h$ is the height. We will find the volume of the rectangular box by substituting the given values in the formula for the volume of a cuboid.

Complete step-by-step solution
The length of the rectangular box is given as $2\text{p}$. The breadth of the rectangular box is given as $4\text{q}$. And the height of the rectangular box is given as $8\text{r}$. As we have the length, breadth, and height, we can say that the rectangular box is shaped as a cuboid. So, to find the volume of the rectangular box, we will use the formula for the volume of a cuboid. The volume of a cuboid is given by
$V=l\times b\times h$
where $l$ is the length, $b$ is the breadth, and $h$ is the height.
 

Now, we will substitute the length, breadth, and height of the rectangular box in the above formula as follows,
${{V}_{box}}=2\text{p}\times \text{4q}\times \text{8r}$
We can rewrite the above equation in the following manner,
${{V}_{box}}=2\times 4\times 8\times \text{p}\times \text{q}\times \text{r}$
Multiplying the number, we get the following,
${{V}_{box}}=64\text{pqr}$
So, the volume of the rectangular box with the given measurements is $64\text{pqr}$.
Therefore, the correct option is (b).

Note: It is important to understand different geometric objects and their areas and volumes. It is essential that we write the formula used for calculation explicitly so that we can avoid making any minor mistakes. Note that the length, breadth, and height given for the rectangular box consists of variables $\text{p, q, r}$. Since no relation or other information regarding these variables, we can treat them as some constant.