Mathematics for Technology: Measurement

1. Course Notes

1.1 Length, Area, and Volume Conversions

• Measurement is crucial in biotechnology and horticulture for lab work, land planning, and designing irrigation systems.

  
  

• Different measurement units are used in various fields (Metric & Imperial systems).

  
  

• Common Length Units: mm, cm, m, km, inch, foot, yard.

• Common Area Units: cm², m², ha (hectare), acre.

• Common Volume Units: cm³, m³, liters, gallons.

• Conversion Formula: 1 m = 100 cm, 1 km = 1000 m, 1 ha = 10,000 m².

  
  

1.2 Conversion Techniques

• Use multiplication or division to convert between units.

• Example: Convert 500 cm to meters.

  • Formula: 500 cm ÷ 100 = 5 meters.

    
    

1.3 Surface Area and Volume of 3D Shapes

• Cube: SA = 6s², V = s³

• Cylinder: SA = 2πr² + 2πrh, V = πr²h

• Sphere: SA = 4πr², V = 4/3πr³

Example: Find the volume of a cylinder with radius 3 cm and height 10 cm.

• Formula: V = π(3)²(10) = 282.74 cm³

2. Quizzes & Exercises

2.1 Multiple-Choice Questions (MCQ)

1. What is the correct conversion of 250 cm to meters?

   • A) 0.25 m

   • B) 2.5 m

   • C) 25 m

   • D) 2500 m

     
     

2. The area of a trapezium is calculated using the formula:

   • A) A = ½ × (a + b) × h

   • B) A = a × b × h

   • C) A = πr²

   • D) A = l × w

     
     

3. A 3-meter tree casts a 1.5-meter shadow. If a building casts a 12-meter shadow under the same conditions, how tall is the building?

   • A) 6 m

   • B) 12 m

   • C) 24 m

   • D) 30 m

     
     

2.2 Fill-in-the-Blank Questions

1. The SI unit for measuring length is the ________.

2. A hectare (ha) is equal to ________ square meters.

3. The volume of a cube is calculated as ________.

   
   

2.3 Problem-Solving Questions

1. Convert 850 mm to meters.

2. Find the perimeter of a rectangle with length 12 m and width 8 m.

3. Calculate the area of a triangle with a base of 10 cm and height of 5 cm.