# Introduction to Mensuration

## What is Mensuration?

Mensuration is an area of Geometry that is concerned with finding the area and volume.

So, we often divide Mensuration in two branches:

• 2 D Mensuration - finding area of 2 D figures, such as a triangle, circle etc.
• 3 D Mensuration - finding volume and surface area of 3 D figures, such as a cube, cone, sphere etc.

We have already covered the 2 D Mensuration part in the Geometry module. Here we will focus solely on 3 D Mensuration.

Here’s a bird’s eye view of all the 3 D solid figures that we are going to deal with:

Now let us understand the terms like Volume, Lateral Surface Area, etc.

## Important Terms in Mensuration

### What is Volume?

Volume of a 3-D (three dimensional) object is the amount of space occupied by it.

To find the volume of any solid, we generally just multiply the area of its base with its height.

We use cubic units to indicate the volume of a solid, e.g. cubic centimeter ($cm^3$), cubic millimeter ($mm^3$), etc.

To measure or indicate the volume of a liquid, we generally use the unit of litre, millilitre, etc.

#### Conversion between units of Volume

1 cubic millimeter ($mm^3$) = 1 mm × 1 mm × 1 mm

1 cubic centimeter ($cm^3$) = 1 cm × 1 cm × 1 cm = 10 mm × 10 mm × 10 mm = 1000 $mm^3$

1 cubic decimeter ($dm^3$) = 1 dm × 1 dm × 1 dm = 10 cm × 10 cm × 10 cm = 1000 $cm^3$

1 cubic meter ($m^3$) = 1 m × 1 m × 1 m = 10 dm × 10 dm × 10 dm = 1000 $dm^3$

1 cubic millimeter = 1 microliter = $10^{-6}$ litre
1 cubic centimeter = 1 millilitre = $10^{-3}$ litre
1 cubic decimeter = 1 litre
1 cubic meter = 1 kilolitre = $10^3$ liters

### What is Lateral Surface Area?

The lateral surface area of a solid object is the area of whole of the object, except the area of its base and top.

To find the lateral surface area of any solid, we generally just multiply the perimeter of its base with its height.

### What is Total Surface Area?

As the name suggests, total surface area of a solid object is the area of whole of the object (including its base and top).

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