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# Math - Geometry Lesson Plans : Surface Area of Cuboids & Cubes

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Mensuration - Formulae for Surface Area of Cuboids & Cubes

A cuboid is a rectangular solid which has six rectangular faces.
A cube is a rectangular solid which has six square faces.

In the figure alongside of the cuboid, length = AB = CD = EF = GH.
In the figure alongside of the cuboid, breadth = AD = BC = EH = FG.
In the figure alongside of the cuboid, height = AE = BF = CG = DH.

 In the figure alongside of the cuboid, diagonal = √ AB2 + BC2 + BF2

 Diagonal of a cuboid = √ Length2 + Breadth2 + Height2

Example
Find the diagonal (in m upto two decimal places) of a cuboid 8 m long, 4 m broad and 2 m high.
Solution.

 Diagonal of a cuboid = √ Length2 + Breadth2 + Height2 = √ 82 + 42 + 22 = 9.17 m.

Total surface area of a cuboid = 2 (Length × Breadth + Breadth × Height + Length × Height)
In the figure alongside of the cuboid, total surface area = 2 (AB × BC + BC × BF + AB × BF).

Example
Find the total surface area (in m2) of a cuboid 8 m long, 4 m broad and 2 m high.
Solution. Total surface area of a cuboid = 2 (Length × Breadth + Breadth × Height + Length × Height)
= 2 (8 × 4 + 4 × 2 + 8 × 2) = 112 m2.

Lateral surface area of a cuboid = 2 (Length + Breadth) × Height
In the figure alongside of the cuboid, lateral surface area = 2 (AB + BC) × BF.

Example
Find the lateral surface area (in m2) of a cuboid 10 m long, 4 m broad and 2 m high.
Solution. Lateral surface area of a cuboid = 2 (Length + Breadth) × Height = 2 (10 + 4) × 2 = 56 m2.

Diagonal of a cube = Ö3 Side
In the figure alongside of the cube, side = AB = CD = EF = GH = AD = BC = EH = FG = AE = BF = CG = DH.
In the figure alongside of the cube, diagonal = √3 AB.

Example
Find the diagonal (in cm) of a cube whose side is 12√3 cm.
Solution. Diagonal of the cube = √3 Side
= √3 × 12√3 = 36 cm.

Total surface area of a cube = 6 × Side2
In the figure alongside of the cube, total surface area = 6 × AB2.

Example
Find the total surface area (in m2) of a cube of side 10 m.
Solution. Total surface area of a cube = 6 × Side2
= 6 × 102 = 600 m2.

Lateral surface area of a cube = 4 × Side2
In the figure alongside of the cube, lateral surface area = 4 × AB2.

Example
Find the lateral surface area (in m2) of a cube of side 12 m.
Solution. Lateral surface area of a cube = 4 × Side2
= 4 × 122 = 576 m2.

Math - Geometry Lesson Plans : Practice Exercise for Surface Area of Cuboids & Cubes

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