Question

Obtain the volume of the rectangular box with given length, breadth and height respectively.
$a,2b,3c$ .
A. $6abc$
B. $6ab$
C. $6-abc$
D. $abc$

Answer 1

Hint: This is the question of mensuration. To find the volume of the box we need to multiply the length, breadth and height together, mathematically it would be represented as $V=l\times b^{\prime }\times h$. The figures which have three dimensions are $3$ Dimensional figures. Volume is the quantity of three-dimensional space enclosed by the closed surface.

Complete step by step solution:
The question asks us to find the volume of the rectangular box, where length is $a$, breadth is $2b$and height of the box is $3c.$To understand it more clearly let us see the model of a rectangular box. Below is the $3-D$ dimension of the rectangular which has been denoted as $l,b^{\prime },h$ to be more precise the length are- $AB,DC,GF,HE$ , the breadth are denoted by- $AH,DG,BE,CF$ , the height are $AD,GH,EF,BC$.

The volume of the rectangular box is denoted by $l\times b^{\prime }\times h$, where $l$ is the length, $b^{\prime }$ is the breadth, $h$ is the height. Applying the same in the given formula we get
$\Rightarrow V=l\times b^{\prime }\times h$
Length is given box is $a$, breadth is $2b$and height of the box is $3c.$ So putting values as $l=a,b^{\prime }=2b,h=3c$ in the above formula we get
$\Rightarrow a\times 2b\times 3c$
On multiplying each these three terms we get:
$\Rightarrow 6abc$
So the volume of the rectangular box is $6abc$.
The correct answer is option $(A)6abc$ when the length, breadth and height is $a,2b$ and $3c$ respectively.

So, the correct answer is “Option A”.

Note: For different solvers the height, breadth and length for rectangular 3D figures may vary, but the volume, total surface area will remain the same. Since the volume is the multiplication of three lengths the unit of the volume will be $uni{t}^3$. Sometimes in question depth is mentioned, so we can use “depth” as ”height” for finding volume or area. In the real world mensuration has a great application.