# Surface Area of a Cube

#### 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.

# 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.

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Total Surface Area & Lateral Surface Area of a Cube [00:11:54]
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