Solids - Cubes and Volumes

Grade 6 · Mathematics

Semester 2 | Period 5 | Week 29

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Subject: Mathematics

Semester: 2

Period: 5

Week: 29

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 29
Lesson Duration: 45 minutes
Week & Period: Week 29, Period 5
Topic: Solids – Cubes and Volumes
Sub-topic: Surface Area and Volume of Cubes

Learning Objectives
By the end of the lesson, students should be able to:
Define cube as a 3D solid with equal edges
Differentiate between surface area and volume
Calculate volume of cubes using formula l³
Apply knowledge of volume to real-life problems

Previous Knowledge
Students already know 2D shapes and perimeter/area of rectangles and squares.

Instructional Materials
Mathematics textbook for Grade 6

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher shows a cube-shaped box and asks learners to describe it.

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

Definition of a Cube

  • A cube is a three-dimensional (3D) solid figure.
  • It has:
    • 6 equal square faces (each face is a square).
    • 12 equal edges (all sides are equal in length).
    • 8 vertices (corners where 3 edges meet).
  • It belongs to a family of solids called polyhedra (shapes with flat faces).

Real-life Examples of Cubes:

  • Dice
  • Sugar cubes
  • Ice cubes
  • Rubik’s cube
  • Small cube-shaped boxes

 

Surface Area of a Cube

  • Definition: The surface area of a cube is the total area of all 6 square faces.
  • Formula:

Surface Area=6l2

where l = length of one edge.

Worked Examples:

  1. A cube has edge l=4 cm.

Surface Area=6l2=6(42)=6×16=96 cm2

  1. A cube with side 10 cm:

Surface Area= 6(102)

6×100=600cm2

  1. A dice with edge 2.5 cm:

Surface Area=6(2.52)=6×6.25=37.5 cm2

Volume of a Cube

  • Definition: The volume of a cube is the space it occupies or its capacity.
  • Formula:

Volume=l3

Worked Examples:

  1. Cube with side l=5 cm

Volume=53=125 cm3

  1. Cube with edge l=6 cm

Volume=63=216 cm3

  1. A box-shaped cube with side l=12 cm:

Volume=123=1728 cm3

 

Practical Applications

  • Surface Area: Used to calculate the amount of wrapping paper, paint, or covering material needed for cube-shaped objects (e.g., wrapping a gift box).
  • Volume: Used to calculate capacity of cube-shaped tanks, cartons, or storage boxes.

Distinguishing:

  • Surface Area → measures the outside covering.
  • Volume → measures the inside space (capacity).

 

Word Problems

  1. A cube has edge 8 cm. Find:
    Its surface area
    ii. Its volume
    • Solution:
      • SA = 6(8²) = 6 × 64 = 384 cm²
      • V = 8³ = 512 cm³
  1. A cube-shaped water tank has side length 1.5 m. Find how much water (in m³) it can hold.
    • V = 1.5³ = 3.375 m³
  2. A cube has surface area 150 cm². Find the length of its side.
    • SA = 6l² = 150 → l² = 150 ÷ 6 = 25 → l = 5 cm

 

Learners’ Activities (Expanded)

  • Learners observe real cube-shaped classroom objects (chalk box, dice, sugar cube).
  • Learners measure edges of small cubes and calculate surface area and volume.
  • Learners draw cube nets (unfolded cube diagrams) and shade the faces.
  • Learners work in pairs to solve given word problems on cubes.
  • Learners compare and contrast surface area vs volume with teacher guidance.

 

Assessment Checks

  1. Define a cube and state its properties.
  2. Find the surface area of a cube of side 9 cm.
  3. A cube has edge 3 cm. Find its volume.
  4. A cube has surface area 294 cm². Find its edge length.
  5. If a cube-shaped carton has volume 1000 cm³, what is the length of each edge?

 

Notes (Expanded & Detailed)

  • A cube is the simplest 3D solid made of squares only.
  • Surface area is measured in square units (cm², m²), while volume is measured in cubic units (cm³, m³).
  • Surface area deals with external covering; volume deals with capacity.
  • In real life:
    • Surface area is useful for wrapping and painting.
    • Volume is useful for storing liquids or objects.
  • Mastering cubes helps in understanding cuboids, cylinders, and other 3D shapes.

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher emphasizes difference between surface area and volume with practical examples.

Evaluation Method (Expanded):
Exit slip/quiz: Find volume of cube with side 8 cm. Teacher will collect slips and provide oral feedback.

Assignment (Expanded):

  1. Find surface area of cube with side 10 cm.
  2. Find volume of cube with side 12 cm.

Follow-up Activity:
Learners measure dimensions of home objects (boxes, cartons) and calculate volume.

Differentiation / Inclusive Strategies
Practical demonstration for struggling learners. Advanced learners solve real-life application problems.

Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low