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Cube and Cuboid

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Cube and Cuboid - Lesson Summary

A cuboid is a solid bounded by six faces that are rectangular in shape. A cuboid whose length, breadth and height are equal is called a cube.

Any two faces other than the opposite faces are called adjacent faces. Any two adjacent faces meet in a line segment, which is called an edge of the cuboid. The point of concurrency of any three edges of a cuboid is called a vertex of the cuboid.

A cube and a cuboid have 8 vertices, 6 faces and 12 edges. Any face of a cuboid may be called the base of the cuboid. In that case, the four adjacent faces of the base are called the lateral faces of the cuboid. Total surface area of a solid is equal to the sum of the areas of all its faces. Area is measured in square units.

Volume of a solid is the measure of the space occupied by it. The volume of substance that can be stored by the object is called its capacity. Volume is measured in cubic units.

If l, b and h are the length, breadth and height of a cuboid respectively, then
        •  lateral surface area = 2h (l + b)
        •  total surface area = 2(lb + bh + lh)
        •  volume = lbh

If 'a' is the length of the edge of a cube, then
        •  lateral surface area = 4a2
        •  total surface area = 6a2
        •  volume = a3



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