Question

The length of a cold storage is double its breadth. Its height is $3$ meters. The area of its four walls (including doors) is $108{m^2}$. Find its volume.

Answer 1

Hint: First, to calculate the length, breadth and height problem we must need to know about the Lateral surface area formula, which can be obtained by twice the height into the length plus breadth.
Given that the length of the cold storage is double its breadth and which can be expressed as $l = 2b$ where $l$ is the length and $b$ is the breadth.

Formula used:
$l \times b \times h$ is the formula to find the total volume of the given problem.
The Lateral surface formula is $2h(l + b)$

Complete step by step answer:
Since given that the that length of the cold storage is double its breadth and which can be expressed as $l = 2b$
Also, the height is given as $3$ meters and which can be expressed as $h = 3$

Hence using the Lateral surface formula is $2h(l + b)$ to find the unknown value of the breadth and length.
Also note that the area of its four walls (including doors) is $108{m^2}$ which is equals to the Lateral surface
Hence, we get $2h(l + b) = 108m$
Since $l = 2b$ then we get $2h(2b + b) = 108 \Rightarrow 2h \times 3b = 108$
Also, since $h = 3$ then we get $2 \times 3 \times 3b = 108$
Further solving we have $18b = 108 \Rightarrow b = 6m$ (by the division operation)
Hence, we get the breadth as $b = 6m$ and thus we have $l = 2b \Rightarrow l = 12m$ is the length.
Therefore, we know the values of the length, breadth and height.
Hence the volume of the cold storage is $l \times b \times h = 12m \times 6m \times 3m$
Using the multiplication, we get $l \times b \times h = 216{m^3}$ which is the required answer.

Note:
Note that while multiplying the numbers like $2m \times 1m$ we can also need to multiply the meters into the meters and it we get the resultant as meter square like $2m \times 1m = 2{m^2}$
Using this method, we have $l \times b \times h = 12m \times 6m \times 3m$ the meter cube as a result. Also using the simple multiplication operation we solved the given problem.