# Measurement - Length, Area, Volume, Density and SI Units

#### PHYSICS REVISION QUESTIONS

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Measurement comprises of length, area, volume, mass, density and time.

## SI Units

Universal System of Units is called system international d' unites (International System of Units) - SI Units.
Below are the major SI Units
Basic Quantity SI Unit Symbol
Length Metre m
Mass Kilogram kg
Time Second s
Electric Current Ampere A
Thermodynamic Kelvin K
Luminous Intensity Candela Cd
Amount of Substance Mole mol

## LENGTH

- The distance between two fixed points.
- The S.I Unit is Metre (M)
Derived units are shown below
Unit Symbol Equivalence in Metres
Kilometre Km 1000
Hectometre Hm 100
Decametre Dm 10
Decimetre dm 0.1
Centimetre Cm 0.01
Millimetre mm 0.001
Micrometre µm 0.000001

Estimating the length of a tree

## AREA

- Measures the surface area covered by a body
- Its unit is m2.
Can you convert 15.5M2 to cm2?

Solution
1m = 100 cm
1m2 = 100 cm x 100 cm = 10000 cm2
15.5 m2 = 15.5 x 10000 cm2
= 1550000 cm2

### Area of a Regular Body

Regular Body Formulae
Square L x L
Rectangle L x W
Circle πr2
Triangle ½bh
Cylinder 2πDh
Trapezium ½(a+b)h

Remember that π = 22/7 or 3.1429

### Area of an Irregular Body

The squares must be 1cm2 each.

Area
Full Squares = .... cm2
½ x Incomplete squares = .... cm2
Area = Full Squares + (½ x Incomplete squares)

## VOLUME

- Measures the amount of space occupied by a body
- Its unit is m3.
Can you convert 4.5m3 to cm3 ?

Remember: 1m3 = 100cm x 100cm x 100cm = 1000000 cm3

### Volume of a Regular Body

Regular Body Formulae

V = S3

V = l x w x h

V = Bh

V = 4/3πr3

V = πr2h

V = 1/3πr2h

#### Right Square Pyramid

V = 1/3S2h
NB: Liquids can be measured by putting them into containers with sizes of graduated objects such as Graduate Cylinder, Syringe, Buret and others

### Volume of an Irregular Body

It can be done using a Measuring Cylinder or a Eureka Can.
##### 1. Measuring Cylinder

Volume = Q (V1) - P (V2)

##### 2. Eureka Can

Volume will be read on the measuring cylinder.

## MASS

- Quantity of matter in a body. SI units is Kilogrammes (Kg)
Mass can be measured using:-
• Top Pan Balance
• Beam Balance
• Lever Balance

## DENSITY

- Mass per unit volume. Its symbol is rho (ρ). Its SI Unit is Kilogramme per Cubic Metre (Kg/m3)
A block of stone has a mass of 140g and is 10cm long, 5 cm wide and 4 cm high. Calculate the density of the stone

Solution

##### Density Using a Density Bottle
The mass of a density bottle is 20g when empty and 45g when filled with water. When filled with liquid x, its mass is 400g. Calculate the density of liquid x. (density of water 1.0 g/cm3)

Solution

### Relative Density

Relative density (RD) is the ratio of the density of a substance to the density of water. It is also known as specific gravity (SG).
- If the value is less than 1, it is less dense than water and would float
- If the value is equals to 1, it has the same density as water
- If the value is greater than 1 it is more dense than water and would sink.

## Measurement I Quiz 1

#### Question - of -

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