Measurement - CSEC Mathematics

Introduction to Measurement

Measurement is the process of assigning numbers to physical quantities like length, area, volume, mass, and time using standard units.

SI Units of Measurement

Quantity SI Unit Symbol
Length Meter m
Mass Kilogram kg
Time Second s
Area Square meter m²
Volume Cubic meter m³

Length and Distance

Length is the measurement of something from end to end.

Metric Units of Length

Unit Equivalent
1 kilometer (km) 1000 meters
1 meter (m) 100 centimeters
1 centimeter (cm) 10 millimeters

Example: Converting Length Units

Convert 3.5 kilometers to meters.

Solution:

1 km = 1000 m

3.5 km = 3.5 × 1000 = 3500 m

Area

Area is the amount of space inside a two-dimensional shape.

Area Formulas

Shape Formula
Rectangle length × width
Square side × side
Triangle ½ × base × height
Circle π × radius²
Parallelogram base × height
Trapezium ½ × (sum of parallel sides) × height
l w base height r

Example: Calculating Area

Find the area of a triangle with base 12 cm and height 5 cm.

Solution:

Area = ½ × base × height = ½ × 12 × 5 = 30 cm²

Volume and Capacity

Volume is the amount of space a three-dimensional object occupies, while capacity is the amount a container can hold.

Volume Formulas

Shape Formula
Cube side × side × side
Cuboid length × width × height
Cylinder π × radius² × height
Sphere (4/3) × π × radius³
Cone (1/3) × π × radius² × height
h l w h r r

Example: Calculating Volume

Find the volume of a cylinder with radius 7 cm and height 10 cm (use π = 22/7).

Solution:

Volume = π × radius² × height = (22/7) × 7 × 7 × 10 = 1540 cm³

Mass and Weight

Mass is the amount of matter in an object, while weight is the force exerted on that mass by gravity.

Metric Units of Mass

Unit Equivalent
1 metric ton (t) 1000 kilograms
1 kilogram (kg) 1000 grams
1 gram (g) 1000 milligrams

Note: In everyday language, people often use "weight" when they mean "mass." In physics, weight = mass × acceleration due to gravity.

Time

Time is the ongoing sequence of events taking place.

Units of Time

Unit Equivalent
1 century 100 years
1 year 365 days (366 in leap year)
1 week 7 days
1 day 24 hours
1 hour (hr) 60 minutes
1 minute (min) 60 seconds

Example: Time Conversion

Convert 3.25 hours to hours and minutes.

Solution:

0.25 hours = 0.25 × 60 minutes = 15 minutes

3.25 hours = 3 hours 15 minutes

Temperature

Temperature is a measure of how hot or cold something is.

Temperature Scales

Scale Freezing Point of Water Boiling Point of Water
Celsius (°C) 0°C 100°C
Fahrenheit (°F) 32°F 212°F
Kelvin (K) 273.15K 373.15K

Conversion Formulas

Example: Temperature Conversion

Convert 25°C to Fahrenheit.

Solution:

°F = (9/5 × 25) + 32 = 45 + 32 = 77°F

Perimeter and Circumference

The perimeter is the distance around a two-dimensional shape, while circumference is the perimeter of a circle.

Perimeter Formulas

Shape Formula
Rectangle 2 × (length + width)
Square 4 × side
Triangle sum of all sides
Circle (Circumference) 2 × π × radius

Example: Calculating Perimeter

Find the perimeter of a rectangle with length 8 cm and width 5 cm.

Solution:

Perimeter = 2 × (length + width) = 2 × (8 + 5) = 2 × 13 = 26 cm

Unit Conversions

Length Conversions

Mass Conversions

Volume Conversions

Example: Unit Conversion

Convert 5 miles to kilometers.

Solution:

1 mile = 1.609 km

5 miles = 5 × 1.609 = 8.045 km

Glossary of Terms

Area
The amount of space inside a two-dimensional shape.
Capacity
The amount a container can hold.
Circumference
The perimeter of a circle.
Mass
The amount of matter in an object.
Perimeter
The distance around a two-dimensional shape.
SI Units
The International System of Units used for measurements worldwide.
Temperature
A measure of how hot or cold something is.
Volume
The amount of space a three-dimensional object occupies.
Weight
The force exerted on a mass by gravity.

Self-Assessment Questions

  1. Convert 2.5 meters to centimeters.

    2. 1 m = 100 cm

    2.5 m = 2.5 × 100 = 250 cm

  2. Calculate the area of a circle with radius 14 cm (use π = 22/7).

    3. Area = π × radius² = (22/7) × 14 × 14 = 616 cm²

  3. Find the volume of a cuboid with length 5 cm, width 3 cm, and height 4 cm.

    4. Volume = length × width × height = 5 × 3 × 4 = 60 cm³

  4. Convert 3 hours 45 minutes to hours in decimal form.

    5. 45 minutes = 45/60 hours = 0.75 hours

    3 hours 45 minutes = 3.75 hours

  5. Calculate the perimeter of a triangle with sides 6 cm, 8 cm, and 10 cm.

    6. Perimeter = sum of all sides = 6 + 8 + 10 = 24 cm

  6. Convert 25°C to Fahrenheit.

    7. °F = (9/5 × °C) + 32 = (9/5 × 25) + 32 = 45 + 32 = 77°F

  7. Find the circumference of a circle with diameter 21 cm (use π = 22/7).

    8. Radius = diameter/2 = 10.5 cm

    Circumference = 2 × π × radius = 2 × (22/7) × 10.5 = 66 cm

  8. Convert 500 grams to kilograms.

    9. 1 kg = 1000 g

    500 g = 500/1000 = 0.5 kg

  9. Calculate the area of a trapezium with parallel sides 8 cm and 12 cm, and height 5 cm.

    10. Area = ½ × (sum of parallel sides) × height = ½ × (8 + 12) × 5 = ½ × 20 × 5 = 50 cm²

  10. Convert 2.5 liters to cubic centimeters (cm³).

    11. 1 liter = 1000 cm³

    2.5 liters = 2.5 × 1000 = 2500 cm³