**Volume and Surface Area:** The **surface area** of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of the arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces.

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**•**Three measures of central tendency of ungrouped data are: (i) mean, (ii) median and (iii) mode.**•**Total surface area of a cuboid = 2[lb + bh + lh]**•**Total surface area of a cube = 6(side)^{2}**•**Lateral surface area of a cuboid = Area of walls of a room = 2(l + b) × h**•**Lateral surface area of a cube = 4a^{2}**•**Curved surface area of cylinder = 2πrh**•**Total surface area of a cylinder = 2πr(r + h)**•**Curved surface area of a cone = πrl**•**Total surface area of a cone = πr(r + l)**•**Surface area of a sphere = 4πr^{2}**•**Curved surface area of a hemisphere = 2πr^{2}**•**Total surface area of a hemisphere = 3πr^{2}**•**Volume of a’cuboid = l × b × h**•**Volume of a cube = (side)^{3}**•**Volume of a cylinder = πr^{2}rh

**SOLIDS AND THEIR SURFACE AREAS**

The bodies occupying space are called solids, such as a cuboid, a cube, a cylinder, a cone, a sphere, etc.

These solids have plane or curved surfaces.

**SURFACE AREA OF A CUBOID AND A CUBE**

The outer surface of a cuboid is made up of six rectangles. If we take the length of the cuboid as l, breadth as b and the height as h, then

Surface area of a cuboid = 2[lb + bh + hl]

Let us recall that a cuboid whose length, breadth and height are equal is called a cube. Let each edge of the cube be �a’, then

Surface area of a cube = 6a^{2}

II. Lateral surface area of a cuboid is 2(l + b)h.

III. Lateral surface area of a cube is 4a^{2}.

IV. Surface area of a cuboid or cube means total surface area.