Measurements of area & Volume
Measurements of area
The amount of surface covered by an object or a place is called its area. The shaded religion in closed in the shapes shown in the figure are these area. The area of a playground is more than that of a classroom and the area of your table top is less than the area of floor of the room.
Unit of area
The standard unit of area in SI system is square metre or metre square ( m²). 1 m² is the area of a square surface whose side is of length 1metre.
The SI unit of area, square metre, is inconvenient to measure very large areas such as the area of a field. We would need larger unit to measure these. Similarly, to measure small areas such as the area of a textbook or that of a coin , we need smaller units. Such unit are called multiple and submultiples of square metre.
Areas of regular shapes
The areas of regular geometric shape can be found by simple measurement and by using the following formulae.
Areas of regular geometric shapes.
| Shape |
Formula |
| Square of side ( a ) |
a² |
| Rectangular of length ( l ) and breadth ( b ) |
lb |
| Triangle of base ( b ) and height ( h ) |
1/2 bh |
| Circle with radius ( r ) |
Ï€r² |
Areas of irregular shapes
Certain object such as a leaf or a feature do not have regular shapes. This areas cannot be determined by using any formula. We can calculate their approximate area by using a square centimetre paper. This paper is divided into equal sized squares of side 1 cm.
Measurement of volume
The space occupied by a substance ( solid, liquid or gas ) is called its volume.
A bucket okay bye more space than a mug.We say dad the volume of a bucket is more than that of a mug . Similarly , as the auditorium is larger than the classroom, we say that the volume of air in the auditorium is more than the volume of air in the classroom.
Unit of volume
The standard unit of volume in the SI system is the cube metre ( m³). It is the volume of a cube with each side of length 1m.
The cube metre is a unit we can use conveniently when we want to measure the volume of air in a room or water in a swimming pool. But to measure the volume of small objections has a notebook or a matchbox, we use smaller units such as cubic centimetre ( cm³). Or cubic millimetres ( mm³).
1m³ = 1m × 1m × 1m × 1m
= 100 cm × 100 cm × 100 cm
= 1000000 cm³
The volume of liquids is measured in called litre ( L ) .
A commonly used submultiple of a litre is milliliter ( ml ).
1 ml = 1 cm³.
1 L = 1000 ml
= 1000 cm³
Also = 1000 L
Measurements of capacity
A liquid has a define volume part not define safe of its own. It takes of the shape of the container into which it is poured. Thus, you can measure the volume of a liquid by pouring it into a container whose inner volume is Known.
The internal volume of a container is Called its capacity. It is equal to the maximum volume of liquid that can be held in the container. Capacity is generally measured in litre or millimetres.
Various kinds of measuring containers of Known capacity are available to measure the volume of a liquid. Each such container has its capacity marked on it. You may have seen milk, oil , kerosene or petrol being measured in cylindrical or conical containers.
These are several devices which are used to measure the volume of liquid in science laboratories. Measuring cylinder , measuring flasks, pipettes and burettes are some of them. Doctors and pharmacists use measuring glass to measure liquid medicines .
The surface of a liquid poured in a measuring cylinder is in the form of a concave or convex curve. This car is called the Meniscus. The reading at the top of a convex meniscus and the bottom of a convex meniscus should be taken to avoid parallax error.
Volume of regular solids
The volume of regular solids can be found by using the following formulae
Volume of regular solids
Volume of irregular solids
The volume of irregular solids cannot be found by using formulae. Therefore, their have to be measured by some other means.
If a solid is completely immersed in a liquid, it displaces a volume of liquid equal to its own volume . This fact is used in finding the volume of irregular solids. The volume of irregular solids can be measured using a measuring cylinder or an overflow jar.
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