Surface area of a cube — lesson. Mathematics State Board, Class 9.

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Cube:

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

Properties of cube:

1. Length, breadth and height all are equal.

2. Each edge of the cube is

$a$ units.

3. It has six square faces.

4. All the vertices are right angle.

5. Opposite sides of the cube are parallel and congruent to each other.

Lateral surface area:

$L. S. A.$

$=$ Area of front side

$+$ Area of back side

$+$ Area of left side

$+$ Area of right side

$= (a \times a) + (a \times a) + (a \times a) + (a \times a)$

$= a^2 + a^2 + a^2 + a^2$

$= 4a^2$

Lateral surface area of the cube

$= 4a^2$ sq. units.

Total surface area:

$T. S. A.$

$=$ Area of top side

$+$ Area of bottom side

$+$ Area of left side

$+$ Area of right side

$+$ Area of front side

$+$ Area of back side

$= (a \times a) + (a \times a) + (a \times a) + (a \times a) + (a \times a) + (a \times a)$

$= a^2 + a^2 + a^2 + a^2 + a^2 + a^2$

$= 6a^2$

Total surface area of the cube

$= 6a^2$ sq. units.

Important!

Total surface area is also called a surface area.

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2. Surface area of a cube