Cube

Cube is one of the box shaped solid object. Six identical square faces are there in the cube. All the faces have 4 edges. A cube contains 12 edges and 8 vertices. A cube is hexahedron, since it has 6 faces. Length, height and weight is used to find the shape of the cube. The base concept of the cube is hypercube. In this article, we will see in detail about the cube.

• The Surface Area of a Cube is 6a²
  
• Volume of a cube is a³
  
• Face diagonal of a cube is $\sqrt{2}$a
  
• Space diagonal of a cube is $\sqrt{3}$a
  
• Radius of a circumscribed sphere is $\frac{\sqrt{3}}{2}$a
  
• Radius of a sphere tangent to edges is $\frac{a}{\sqrt{2}}$
  
• Radius of an inscribed sphere is $\frac{a}{2}$
  
• Angles between faces of a cube is $\frac{\pi}{2}$

These formulas are used to find the volume, area and height of a cube.

Below are some examples based on the cube

Example 1: Find the volume of the cube, whose side a is 9?

Solution: Given side length(a) = 9 units

Formula for finding the volume of the cube:

Volume of a cube = a³

= 9 x 9 x 9

= 729 cubic units

Example 2: Find the Surface area of a cube of side length 8 cm?

Solution: Given side length(a) = 8cm

Formula for finding the surface area of cube:

Surface area of cube = 6 a²

= 6 (8)²

= 6 (64)

= 384 cm²