A cube is a solid figure where the dimensions length, breadth, and height are equal. In this article, we calculate the volume and surface area of a cube. Here the students of grade 9 can know the definition of volume of the cube, the surface area of a cube with suitable formulas, examples. By using all these you can learn in-depth about the surface area and volume of a cube and also score good marks in the exams.
Volume and Surface Area of Cube
Surface Area of Cube: The surface area of a cube is defined as the sum of the areas of all the faces of a cube.
An example of the surface area of a cube is die.
Volume of a cube: The volume of a cube is defined as the total space occupied by the solid cube. It is the multiplication of all the dimensions such as length, breadth, and height. The lengths of all the dimensions in a cube are equal. Thus the formula of volume of a cube is a³.
Surface Area and Volume of a Cube Formula
S.A of a cube Formula:
The formula of the surface area of a cube is 2 × length × breadth + 2 × length × height + 2 × breadth × height
We know that,
All the sides in a cube are equal
length = breadth = height = a
Surface Area of a cube = 2 × a × a + 2 × a × a + 2 × a × a
= 2 a² + 2 a² + 2 a²
= 6a²
Thus the Surface Area of a cube is 6a²
Volume:
Volume of a cube = lbh
V = (a)³
Also, Check:
Volume and Surface Area of Cube Example Problems
Example 1.
The cube of edge 3 cm is divided into cubes of edge 1 cm. How many cubes will be made? Find the total surface area of the smaller cubes.
Solution:
Given,
The cube of edge 3 cm is divided into cubes of edge 1 cm.
The volume of the bigger cube = (s)³
= 3³ cm³
= 27cm³
We know that,
The volume of each of the smaller cubes = (s)³
= 1³ cm³
= 1 cm³
Therefore, the number of smaller cubes = 27cm³/1cm³
= 27
We know that,
The total surface area of a smaller cube = 6(s)²
= 6 × 1 cm²
= 6
Therefore, the total surface area of the eight smaller cubes = 27 × 6 cm² = 162cm²
Example 2.
The cube is 3.5 inches on each side. Find its volume and surface area.
Solution:
Given that
Cube = 3.5 inches
We know that,
The volume of cube = s³
The volume of cube = (3.5)³
= 42.875 cubic inches
We know that,
The surface area of the cube = 6s²
The surface area of the cube = 6(3.5)²
= 6 × 12.25
= 73.5 square inches
Example 3.
A block is a cube measuring 6 inches on each side. Find the volume and surface area of the cube.
Solution:
Given that
Cube = 6 inches
We know that,
The volume of cube = s³
The volume of cube = (6)³
= 216 cubic inches
The surface area of the cube = 6s²
The surface area of the cube = 6(6)²
= 6 × 36
= 216 square inches
Therefore the surface area of the cube is 216 square inches
Example 4.
A note cube measures 2 inches on each side and finds its volume and surface area.
Solution:
Given that
Cube = 2 inches
We know that,
The volume of cube = s³
The volume of cube = (2)³
= 8 cubic inches
The surface area of the cube = 6s²
The surface area of the cube = 6(2)²
= 6 × 4
= 24 square inches
Therefore the surface area of the cube = 24 square inches
Example 5.
The cube is 4 inches on each side. Find its volume and surface area.
Solution:
Given that
Cube = 4 inches
We know that,
The volume of cube = s³
The volume of cube = (4)³
= 64 cubic inches
The surface area of the cube = 6s²
The surface area of the cube = 6(4)²
= 6 × 16
= 96 square inches
Therefore the area of the cube is 96 square inches.
FAQs on Volume and Surface Area of Cube
1. Is the surface area and volume of a cube the same?
We know that the volume of a cube is equal to s3, where s is the length of a given side of the cube. The sides of a cube are all the same, the surface area of the cube is equal to 6 times the area of one face.
2. Is surface area equal to volume?
The increase in volume is always greater than the increase in surface area.
3. What is volume and surface area?
The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.