Sample Problems on Cube Faces Edges and Vertices

Problem 1: Find the surface area of the cube if its side is 6 cm

Solution:

Given: 

Side of the cube = 6 cm

As we know that

Surface area of the cube = 6 × side × side

⇒ Surface area of the cube = 6 × side²

⇒ Surface area of the cube = 6 × 6²

⇒ Surface area of the cube = 216 cm²

Therefore,

Surface area of the cube is 216 cm².

Problem 2: Find the volume of the cube if its side is 4 m².

Solution:

Here we need to find the volume of the cube

Given:

Side of the cube = 4 m²

As we know that

Volume of the cube = Side × Side × Side

⇒ Volume of the cube = Side³

⇒ Volume of the cube = 4³

⇒ Volume of the cube = 4 × 4 × 4

⇒ Volume of the cube = 64 m³

Therefore,

Volume of the cube is 64 m³.

Problem 3: Find how many small cubes can be made from a big cube of side 16 m in small cubes of side 4 m

Solution:

Here we need to find out how many small cubes can be made out of one big cube.

As we know that

Volume of cube = Side³

⇒ Volume of big cube = Side × Side × Side

⇒ Volume of big cube = 16 × 16 × 16

⇒ Volume of big cube = 16³

⇒ Volume of big cube = 4096 m³

Further,

Volume of small cube = Side × Side × Side

⇒ Volume of small cube = 4 × 4 × 4

⇒ Volume of small cube = 4³

⇒ Volume of small cube = 64 m³

Now,

Number of small cubes that can be made from the big cubes = Volume of big cube/Volume of small cube

⇒ Number of small cubes = 4096/64

⇒ Number of small cubes = 64

Therefore,

64 small cubes will be made out of the big cube.

Problem 4. If the surface area of a cube is 486 m². Then find the volume of the cube.

Solution:

Here we need to find the volume of the cube from a given surface area

Given that Surface area of the cube = 486 m²

As we know that

Surface area of the cube = 6 × Side²

⇒ 486 = 6 × Side²

⇒ Side² = 486/6

⇒ Side² =  81

⇒ Side = √81

⇒ Side = 9 m

Now,

Volume of cube = Side³

⇒ Volume of cube = 9³

⇒ Volume of cube = 9 × 9 × 9

⇒ Volume of cube = 729 m³

Therefore,

Volume of the cube is 729 m³.

Cube is a 3-Dimensional Figure in which all dimensions are equal. A cube has 6 Square faces as all the sides of a cube are equal. The boundary where the faces of the cube meet are called the cube edges. The point at which the cube edges meet is called the cube vertices. A cube has 12 Edges and 8 vertices. In this article, we will learn about cube edges faces vertices in detail with a brief introduction to cubes.