Volume of a Cubical Box
The volume of a cubical box is the amount of space inside the cubical box. What is the volume of a cubical box and how do you define it? Let us understand this with an example. As you walk into a cafe and order a juice, you get to choose between three variants, regular, medium, and large. What is it that’s different between these three choices? Well, one look at the glasses that are used to serve them tells you that the only thing different is the amount of juice contained within! Volume is nothing but the space an object occupies. An object with a larger volume occupies more space. Let's learn how to find the volume of a cubical box and its volume in detail here with the help of few solved examples and practice questions.
| 1. | What is Volume of a Cubical Box? |
| 2. | Volume of a Cubical Box Formula |
| 3. | How to Find the Volume of a Cubical Box? |
| 4. | FAQs on Volume of a Cubical Box |
What is Volume of a Cubical Box?
The volume of a cubical box is the number of unit cubes that can be fit into it. A cubical box is a cube that is a 3D solid object with six square faces. As it resembles a cube and we know all the sides of a cube are of the same length, so is the case with a cubical box. The cube is also known as a regular hexahedron and is one of the five platonic solids. The unit of volume of the cubical box is given in "cubic units". For example, it can be expressed as m3, cm3, in3, or ft3, etc depending upon the given units. Let us see how to find the formula of the volume of a cubical box.
Volume of a Cubical Box Formula
The volume of a cubical box is calculated in the same way as the volume of cube. Thus, it can be easily found out by just knowing the length of the edge of the cubical box.
If the length of the cubical box is "s", then its volume will be: \( \text s \times \text s \times \text s = \text s^3 \)
For example, The volume of a cube-shaped dice of length 5 inches can be found out as:
Volume of the dice = \(5\;\text{in} \times 5 \;\text{in}\times 5\;\text{in} = 5^3 \;\text {in}^3 = 125 \text { in}^3\)
By the above formula, we can say that the volume of a cubical box is directly proportional to the cube of its sides, for example: If the side of the cube becomes double, then the volume becomes eight times.
How To Find the Volume of a Cubical Box?
As we learned in the previous section, the volume of a cubical box with side 's' is V = s3. Thus, we follow the below steps to find the volume of a cubical box.
- Step 1: Identify the length of the side and name it to be "s".
- Step 2: Find the volume using the formula V = s3.
- Step 3: Represent the final answer with cubic units.
Example: Find the volume of a cubical box of side 3 units.
Solution: Given the length of the side of the cube is s = 3 units.
Its volume is, V = s3
⇒ V = (3)3
⇒ V = 27 cubic units.
Therefore, the volume of the given cubical box of side 3 units is 27 cubic units.
FAQs on Volume of a Cubical Box
What Is the Volume of a Cubical Box?
The volume of a cubical box is defined as the amount of space inside it. A cubical box is a 3-D solid object with six square faces. All the sides of a cube are of the same length. The cube is also known as a regular hexahedron and is one of the five platonic solids.
How Do You Find the Volume of a Cubical Box?
We can find the volume of a cubical box using the following steps:
- Step 1: Identify the value of the length of the side of the cubical box.
- Step 2: Cube the value.
- Step 3: The answer obtained is the volume of the cubical box which is written with its unit.
What Is the Volume of a Cubical Box of Side 10 cm?
We know that the side of the cylinder is s = 10 cm. Thus, the volume of the cubical box is given by using V = s3.
V = (10)3
⇒ V = 1000 cm3
Thus, the volume of a cubical box of side 10 cm is 1000 cm3.
What Units Are Used With the Volume of a Cubical Box?
The units used to measure the volume of a cubical box are m3, cm3, in3, or ft3, etc depending upon the given units.
What Is the Volume of a Cubical Box and a Cuboidal Box?
The volume of a cubical box is calculated by finding the cube of the side length and the volume of the cuboidal box is found out by finding the product or length width and height of the cuboidal box. We can also use the formulas volume of cubical box = s3, and volume of cuboidal box = (length × breadth × height).
What Is the Formula for Finding the Volume of a Cubical Box?
The formula to find the volume of a cubical box whose side is s is given by the formula, V = s3. i.e., the volume directly varies with the cube of the side length.