While learning geometry students usually have to find the volume and the surface area of a cube. To accomplish the task, the student needs to memorize and understand the application of formulas that apply to these three-dimensional figures. The volume of cube refers to the amount of space inside a cubic object, measured in cubic units, while surface area measures the total amount in square units of each object’s six faces. It is also important to state your answer using the proper units, since not doing so will typically result in completely wrong calculation.
What is a Cube?
A cube is a three-dimensional object that has six congruent square faces. Dimensions of all the 6 square faces of the cube are the same. A cube is sometimes also referred to as a regular hexahedron or as a square prism. It is one of the 5 platonic solids. Some real-life examples of a cube are an ice cube, a Rubik’s cube, a regular dice, etc. Let us learn about a cube along with the formulas to find the volume and area of a cube.
How To Find the Volume of a Cube?
Computing the volume of a cube is easy. Because all sides of a cube are equal, the volume formula is V = s³., where “s” is the length of one side. For example, if the cube had an edge spanning 4 inches, its volume would be 4³. or 64 cubic inches.
The volume of a cube can be easily found out by just knowing the length of its edge or the measure of its diagonal. Different steps followed to calculate the area of the cube depending upon the given parameters will be covered in this section.
Volume of Cube Using Edge Length
The measure of all the sides of a cube is the same. Thus, we only need to know one side in order to calculate the volume of a cube. The steps to calculate the volume of a cube using the side length are,
Step 1: Note the measurement of the side length of the cube.
Step 2: Apply the formula to calculate the volume using the side length: Volume of cube = (side)³.
Step 3: Express the final answer along with the unit(cubic units) to represent the obtained volume.
Volume of Cube Using Diagonal
Given the diagonal, we can follow the steps given below in order to find the volume of a given cube.
- Step 1:Note the measurement of the diagonal of the given cube.
- Step 2:Apply the formula to find the volume using diagonal: [√3×(diagonal)3]/9
- Step 3:Express the obtained result in cubic units.
Surface Area of a Cube
Surface area of cube is the sum of areas of all the faces of the cube that covers it. The formula for surface area is equal to six times the square of length of the sides of the cube. It is represented by 6a², where a is the side length of the cube.It is basically the total surface area.
Surface Area of Cube Formula is Area = 6 × a². Because each face has a surface area of s^2 and every cube has six faces. For example, if a cube has an edge of 5 cm, the surface area would be 6*5² or 150.
Add the proper units to your answer. In the example, you would write, “150 square cm.”