Question

The formula for finding the volume of the cuboid:

Answer 1

Hint: By finding out the volume of the cuboid, we come to know about the capacity of the cuboid. So for proving the volume of the cuboid, its surface area should be known. Then surface area will be multiplied by the height of the cuboid and after multiplying them we come to know about the volume of the cuboid.

Complete step by step answer:
Volume of the cuboid is defined as the quantity which is used to find out the space in a cuboid. A cuboid is the three dimensional structure which has 6 rectangular faces. A rectangle has $6$faces, $8$vertices and$12$edges. Opposite faces of the cuboid are parallel and equal. Volume of the cuboid will be measured in cubic units. Any surface can be considered as the base of the cuboid and the remaining four faces which are adjacent to the base are known as lateral faces. The face opposite to the base is known as the top face of the cuboid.
Various examples of cuboid are books, bricks and duster.

Volume of the cuboid with length ‘l’ breadth ‘b’ and height ‘h’ is given by,
Proof of the formula:
Volume of the cuboid is given by multiplying the product of one of the surfaces of the cuboid to the height of the cuboid.
We know that the surface area of the one face of the cuboid is given by multiplying the length and breadth of the cuboid.
So, surface area will be given as:
$\Rightarrow surface\text{ }area=length\times breadth$
So, volume will be given as:
$\Rightarrow volume=length\times breadth\times height$
For example, suppose there is a cuboid of length$\text{5 }cm$ , breadth$6\text{ }cm$ and height $8\text{ }cm$ then volume of the cuboid will be.
\[\begin{align}
  & \Rightarrow volume=length\times breadth\times height \\
 & \Rightarrow volume=5\text{ }cm\times 6\text{ }cm\times 8\text{ }cm \\
 & \Rightarrow volume=240\text{ }c{{m}^{3}} \\
\end{align}\]
Volume of the cuboid is used when we have to find out the volume of water or anything that is filled in an object which is of the shape of the cuboid.

Note: A cuboid having equal measurements of length, breadth and height is known as the cube. By knowing the volume of the cuboid we can also find out its density. The volume of the cuboid can be of any unit .It can be in\[c{{m}^{3}}\],\[{{m}^{3}}\] or\[m{{m}^{3}}\]. If the length, breadth and height are given in different units, then we will first change them into the same units and then we will solve the question else the answer will be wrong.