how to find the volume of a square

Volume of a Square Box

The volume of a square box is the space occupied by the square box or the cube. A square box is a three-dimensional solid object which has the shape of a cube, and a cube is a 3-D solid object with six square faces. The cube is also known as a regular hexahedron and is one of the five platonic solids. In this section, we will learn about the volume of a square box along with a few solved examples and practice questions.

What Is the Volume of a Square Box?

The volume of a square box (V) can be defined as the space occupied by the square box or the cube. We can find the volume of a square box just by knowing the length of the side of the box. The volume of a square box is equal to the cube of the length of the side of the square box.

The formula for the volume is V = s³ , where "s" is the length of the side of the square box.

Volume of a Square Box Formula

The volume of the square box is equal to the cube of the side length of the box. The formula for the volume of the square box is V = s³, where s is the length of the side of the box. We can also calculate the volume of the square box or cube if we know the length of the diagonal of the box.

The formula for the volume of the square box or cube with diagonal length ′d′ is V = (√3 × d³)/9

Volume of a square box formula

Calculation of Volume of a Square Box

The volume of the square box is equal to V = s³. By following the steps mentioned below we can find the volume of a square box.

Step 1: Calculate the length of any side of the box.
Step 2: Find the cube of the side length. Or, use the formula V = (√3 × d³)/9 when the diagonal length 'd' is known.
Step 3: Represent the answer in cubic units of the length.

Important Notes on Volume of a Square Box

Volume of a square box when its side s is given, V = s³
Volume of a square box when length of its diagonal d is given, V = (√3 × d³)/9
Volume of a square box when its base area and height are given, V = Base area × Height

Related Topics on Volume of a Square Box

Volume of Prism
Volume of Rectangular Prism
Volume of Cube Calculator

Solved Examples on Volume of a Square Box

Example 1: The length of the side of a square box is 5 in. Find the volume of the square box.

Solution:

Length of the side, s = 5 in

Using the formula for the volume of the square box: V = s³
⇒ V = 5³
⇒ V = 125

Answer: Volume of the square box is 125 cubic inches.
Example 2: The length of the diagonal of a square box is √3 units. Find the volume of the box.

Solution:

Length of the diagonal = √3 units

Using the formula for the volume of the square box: V = (√3 × d³)/9
⇒ V = [√3 × √(3³)]/9 = 1

Answer: Volume of the box is 1 cubic unit.

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Practice Questions on Volume of a Square Box

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FAQs on Volume of a Square Box

What Is Meant By the Volume of a Square Box?

The volume of a square box refers to the total space occupied by the square box in a three-dimensional plane. It is expressed in cubic units.

What Are the 3 Ways To Find the Volume of a Square Box?

The three ways to find the volume of a square box are as following,

Method 1: Using the formula of volume with the length of an edge given: V = s³
Method 2: Using the formula of volume where the length of the diagonal is given: V = (√3×d³)/9
Method 3: Multiplying the base area with the height of the object: V = base area × h

What Is the Formula of Volume of the Square Box?

The volume of a square box can be calculated using the side length of the box. The volume of the square box is equal to s³, where 's' is the length of the box.

Is Volume of Square Box Measured in Square Units?

No, the volume of a square box is not measured in square units, rather it is calculated in cubic units, using units like cm³, in³, m³, ft³, etc.

What Is a Square Box?

A 3-D object which has six square faces is called a square box and is also known as a cube.

How Many Vertices Are There in a Square Box?

There are 8 vertices in a square box. A square is a cube with 8 vertices, 6 faces and 12 edges.

How Many Faces Does a Square Box Have?

A square box has 6 faces that is why it is also known as hexahedron and is one of the platonic solids.