# Introduction

**Volume and Surface Area of Solids**

**Solids**

Bodies occupying space and having definite shapes are called solids.

**Cuboid**

A solid which is bounded by six rectangular plane faces. Example: Match box, brick, tile, book, tea packet, etc.

A cuboid has six rectangular faces, 8 vertices and 12 edges.

**Cube**

A cuboid whose length, breadth and height are equal. e.g. ice cube, ludo dice, sugar cubes.

Each edge of a cube is equal and all the six faces of a cube are equal to each other in all respects.

**Right Circular Cylinder**

If we rotate a rectangle about one of its sides, the solid thus formed is called right cylinder. A cylinder has a uniform circular cross-section and its lateral surface is a curved surface. The top and the bottom of the cylinder are in circular form.

**Example**

Road roller, gas cylinder, powder container, water pipe, wire, round pencil, beaker, pillars, a well, etc.

Radius of the base of the cylinder is called the radius of the cylinder.

The distance between two circular ends of the cylinder is called the height of the cylinder.

If we open the curved surface of the cylinder, it will be in the rectangular form.

**Cone**

If we rotate a right angled triangle about one of its side, a solid will be formed. This solid is called a cone e.g. Ice cream cone, a clown cap, a tapered end of the pencil, a conical tent, conical flask.

If we join the vertex (A) of the cone to the centre of the base (O), then this length is called height of the cone.

The radius of a circular base of a cone is called the radius of the cone.

A cone is also defined as a solid having a plane circular base and whose lateral surface is a curved surface tapering into a point. This point is called the vertex of the cone.

# Sphere

Any object in the form of a ball is called sphere. Sphere is a set of points in the space equidistant from a fixed point. This fixed point is called the centre of the sphere and the distance between the centre and any point on the surface of the sphere, is called the radius of the sphere.

**Diameter of the Sphere **

A line segment passing through the centre of the sphere with its end points on the sphere.

**Hemisphere**

Any plane passing through the centre of a sphere divide the sphere in two equal parts, each part is called a hemisphere.

**Unit of Volume**

The volume of a cube of 1 cm sides is called 1 cubic centimetre.

1000 mm^{3 }= 1 cm^{3}(1 cm = 10 mm)

1000 cm^{3} = 1 dm^{3} (1 dm = 10 cm)

1000 dm^{3 }= 1 m^{3}(1 m = 10 dm)

10^{9} m^{3 }= 1 km^{3}(1 km = 1000 m)

1 litre = 1 l = 1 dm^{3 }= 1000 cm^{3}

1 millilitre = 1 ml = (.001) l = 1 cm^{3}

1 kilolitre = 1000 l = 1 m^{3}.