VOLUME OF A CUBOID WITH EXAMPLES AND FAQ

Volume of Cuboid

What is a Cuboid?

A cuboid is a three-dimensional geometrical figure having six rectangular faces. Its opposite faces are always parallel and equal. Cuboid comprises 6 faces, 8 vertices and 12 edges. Some Examples of cuboids are Bricks, Books, Erasers, Wallets, etc.

In geometry, the volume of any shape is the amount of space it occupies in a 3-dimensional space. The volume of a cuboid is the parameter that measures the 3D(three-dimensional) space in a cuboid. The volume of a cuboid is measured in cubic units, for example, {\text m}^{3}, {\text {dm}}^{3},etc.

The volume of a cuboid having Length → L, Breadth → B and Height → H is given by the formula:

\text { Volume of cuboid }=L \times B \times H=L B H \text { cubic units }

Volume of Cuboid Formula Derivation

The concept of rectangular sheets being up piled up, one on top of the other can be used for deriving the formula for the volume of a cuboid. The area of a rectangular sheet is ‘a’, where a = l × b. Let the height up to which the sheets are stacked be ‘h’ and the volume of the cuboid be ‘V’. Then, the volume of the cuboid is given by multiplying the area of a rectangular sheet and height.

\text{The volume of cuboid} = \text{area of a single rectangular sheet} \times \text{Height}

\text{The area of the rectangular sheet} =l \times b

\text{Hence, the volume of a cuboid}, \mathrm{V}=\mathrm{l} \times \mathrm{b} \times \mathrm{h}=\mathrm{lbh}

Total Surface Area 

The Total Surface Area of a cuboid is equivalent to the sum of the areas of all the six rectangular faces. The unit of measurement of the area is square units, for example, {\text m}^{2}, {\text{mm}}^{2}, \text { etc. }The formula for the total surface area of a cuboid whose length is ‘l’, breadth is ‘b’ and height is ‘h’, is:

Total surface area of a cuboid is =2[(l\times  b)+(h \times b)+(l \times h)]\text{ square units} =2(lb+hb+lh)\text{ square units}

Lateral Surface Area of Cuboid

The Lateral Surface Area of a cuboid is equivalent to the sum of the four rectangular faces. Here, the area of the rectangular faces of the top and bottom faces are excluded. The formula for the lateral surface area of a cuboid whose length is ‘l’, breadth is ‘b’ and height is ‘h’, is:

\text { Lateral Surface Area of a Cuboid }=2 h(l+b)

The volume of a Cube

A cube is a special case of a cuboid where all the sides are equal in dimension.

The volume of a cube with side length a =a \times a \times a=a^{3}

EXAMPLES

Example 1: Calculate the amount of air that is present in a room that has a length of 10 m, breadth of 8 m and a height of 12 m.

Solution: 

Amount of air that is present in a room = capacity of the room.

As the room is similar to a cuboid hence the capacity of the room can be calculated by using the formula of volume of cuboid.

\therefore \text { Volume of cuboid }=\mathrm{l} \times \mathrm{b} \times \mathrm{h}=(10 \times 8 \times 12) \mathrm{m}^{3}=960 \mathrm{~m}^{3}

Thus, the amount of air the room can accommodate is 960{\text{ m}}^{3}.

Example 2: What will be the height of the cuboid if its volume is 1200 \mathrm{~cm}^{3}, length is 40 cm and breadth is 15 cm?

Solution: 

The formula for the volume of a cuboid is known to us and it is:

Volume = Length × Breadth × Height.

Volume = 1200 \mathrm{~cm}^{3},

Length = 40 cm

Breadth = 15 cm

Let the height of cuboid be y cm.

Volume = Length × Breadth × Height

\Rightarrow \text { Volume }=(40 \times 15 \times \mathrm{y}) \mathrm{cm}^{3}=1200 \mathrm{~cm}^{3}

\Rightarrow y=\frac{1200}{40 \times 15} \mathrm{~cm}=\frac{1200}{600} \mathrm{~cm}=2 \mathrm{~cm}

\therefore  \text{ The  height of cuboid is } 2 \mathrm{~cm}.