Advertisement Remove all ads

Surface Area of a Cube

Advertisement Remove all ads

Topics

definition

  • Cube: A cube is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meetings at each vertex. The cube is the only regular hexahedron (i.e., a solid figure with six plane faces) and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.
  • Lateral surface area of the cube: Out of the six faces of a cube, we only find the area of the four faces, leaving the bottom and top faces. In such a case, the area of these four faces is called the lateral surface area of the cube.

formula

  • Total surface area of the cube = 6a2.
  • Lateral surface area of a cube = 4a2.

notes

Cube:

A cube is a cuboid whose edges are all of equal length. A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron (i.e., a solid figure with six plane faces) and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.

Total surface area of cube:

Cube is a cuboid, whose length, breadth, and height are all equal.

Let, Length = breadth = height = a

Total surface area of the cube = 2(a × a + a × a + a × a)

Total surface area of the cube = 2 × (3a2)

Total surface area of the cube = 6a2

Lateral Surface area of cube:

Suppose, out of the six faces of a cube, we only find the area of the four faces, leaving the bottom and top faces. In such a case, the area of these four faces is called the lateral surface area of the cube.

lateral surface area of a cube of side a is equal to 4a2.

Lateral surface area of a cube = 4a2.

Example

One side of a cubic box is 0.4 m. How much will it cost to paint the outer surface of the box at the rate of 50 rupees per sqm?

side = l = 0.4 m.

Total surface area of cube = 6 × (l)2
= 6 × (0.4)2
= 6 × 0.16
= 0.96 sqm

Cost of painting 1 sqm is 50 rupees.

∴ Cost of painting 0.96 sqm will be = 0.96 × 50 = 48 rupees

It will cost 48 rupees to paint the outer surface of the box.

If you would like to contribute notes or other learning material, please submit them using the button below.

Shaalaa.com | Total Surface Area & Lateral Surface Area of a Cube

Shaalaa.com


Next video


Shaalaa.com


Total Surface Area & Lateral Surface Area of a Cube [00:11:54]
S
Series: Surface Area of a Cube
0%


Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×