Volume of Cuboid

The volume of a cuboid is the quantity that is used to measure the space in a cuboid. The cuboid is a three-dimensional shape that can be seen around us very often. In this short lesson, we will learn to find the volume of a cuboid. We will also learn to deduce the formula of volume of cuboid using a rectangular sheet and understand how to apply the formula as well. Once you understand this chapter you will learn to solve problems on the volume of the cuboid.

1.	What Is the Volume of Cuboid?
2.	Volume of Cuboid Formula
3.	How to Calculate the Volume of Cuboid?
4.	FAQs on Volume of Cuboid

What Is the Volume of Cuboid?

The volume of the cuboid is the measure of the space occupied within a cuboid. The cuboid is a three-dimensional shape that has length, breadth, and height. If we have a rectangular sheet and we go on stacking such sheets, we will end up getting a shape that has some length, breadth, and height. This stack of sheets looks like a shape that has 6 faces, 12 edges, and 8 vertices hence giving us the shape of a cuboid. The unit of volume of cuboid is given as the (unit)³. The metric units of volume are cubic meters or cubic centimeters while the United States Customary System (USCS) units of volume are, cubic inches or cubic feet. The volume of the cuboid depends on the length, breadth, and height of the cuboid, hence changing any one of those quantities changes the volume of the shape.

Volume of Cuboid Formula

The formula for the volume of the cuboid can be derived from the concept explained on rectangular sheets. Let the area of a rectangular sheet of paper be 'A', the height up to which they are stacked be 'h' and the volume of the cuboid be 'V'. Then, the volume of the cuboid is given by multiplying the base area and height.
The volume of cuboid = Base area × Height
The base area for cuboid = l × b
Hence, the volume of a cuboid, V = l × b × h = lbh

How to Calculate Volume of Cuboid?

The volume of a cuboid is the space occupied inside a cuboid. If all the three dimensions of a cuboid get equal, it becomes a cube. The volume of the cuboid can be calculated using the formula of the volume of the cuboid. The steps to calculate the volume of a cuboid are:

Step 1: Check if the given dimensions of cuboids are in the same units or not. If not, convert the dimensions into the same units.
Step 2: Once the dimensions are in the same units, multiply the length, breadth, and height of the cuboid.
Step 3: Write the unit in the end, once the value is obtained.

Let us take an example to learn how to calculate the volume of a cuboid using its formula.

Example: Find the volume of the cuboid having a length of 7 inches, breadth of 5 inches, and height of 2 inches.
Solution: As we know, the volume of a cuboid, V = lbh
Here, length l = 7 inches, breadth b = 5 inches and height h = 2 inches
Thus, volume of cuboid, V = lbh = (7 × 5 × 2) in³
⇒ V = 70 in³
\(\therefore\) The volume of cuboid is 70 in³.

Volume of Cuboid Examples

Example 1: If the dimensions of a cuboidal fish aquarium are, 30 inches, 20 inches, and 15 inches. Can you determine the volume of the fish aquarium?
Solution: As we know, the fish aquarium is of cuboidal shape. Hence, the dimensions of the fish aquarium are:
Length of the aquarium = 30 in
Width of the aquarium = 20 in
Height of the aquarium = 15 in

The volume of the aquarium is given as:
Volume = Length × Width × Height
⇒ Volume = 30 × 20 × 15 in³= 9000 in³
∴ The volume of the cuboidal fish aquarium is 9000 cubic inches.
Example 2: What will be the length of the cuboid if its volume is 3000 in³, breadth is 15 inches and height is 10 inches?
Solution: As we know, volume of a cuboid is given as Volume = Length × Breadth × Height. The given dimensions for cuboid are:
Volume = 3000 in³
Breadth = 15 in
Height = 10 in
Let the length of cuboid is x inches.

Hence, the volume of the cuboid will be:
Volume = Length × Breadth × Height
⇒ Volume = x × 15 × 10 = 3000 in³
⇒ x = (3000/(15 × 10)) = 20 in
∴ The length of cuboid is 20 inches.
Example 3: Find the volume of cuboid if the length is 10 in, breadth is 20 in, and height is 30 in.

Solution: volume of a cuboid is given as Volume = Length × Breadth × Height. The given dimensions for cuboid are:
Length = 10 in
Breadth = 20 in
Height = 30 in
⇒ Volume = 10 × 20 × 30 in³= 6000 in³
∴ The volume of the cuboid is 6000 cubic inches.

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Practice Questions on Volume of Cuboid

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FAQs on Volume of Cuboid

What Do You Mean by Volume of Cuboid?

The volume of a cuboid is the space that is enclosed within a cuboid. For example, in order to fill water in an aquarium, we must know its volume.

How to Find the Volume of Cuboid?

The volume of a cuboid is calculated by multiplying its length, width, and height. For example, the volume of a cuboid of length, width, and height 2 inches, 3 inches, and 4 inches is given as Volume = length × width × height = 2 × 3 × 4 = 24 inch³

What Is the Formula for the Volume of Cuboid?

The formula of volume of a cuboid is = Length × Width × Height. The formula for the volume of cuboid is deduced by stacking rectangular sheets one over another thereby giving us three parameters in the formula length, width, and height.

If the Units of Dimensions of a Cuboid Are Different, Then How to Find the Volume of Cuboid?

If the units of the given dimensions of a cuboid are different, then first we would need to change the units of dimensions of any two dimensions in the unit of the third dimension. After that, multiply all three dimensions known to us, to calculate the volume of the cuboid.

Does the Order of Height, Width, and Length Matter While Calculating the Volume of Cuboid?

No, the order of height, width, and length does not matter while finding a cuboid's volume because we need to multiply all three quantities for determining it. As multiplication is associative, hence, no matter in whichever order dimensions are multiplied the volume of the cuboid remains the same.

How Does the Volume of Cuboid Change When the Length of Side Is Halved?

The volume of the cuboid gets half when the length of the side is halved as l = l/2. As, volume of cuboid = length × width × height = (l/2)× b × h = (lbh)/2 = volume/2. Thus, the volume of the cuboid gets halved as soon as its length gets halved.

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