Lesson 4: Volume of Solids and Compound Shapes

👨🏽‍🏫 Introduction

Have you ever tried filling a water tank, pouring juice into a bottle, or buying a bag of cement? What you’re really dealing with is volume — the amount of space an object takes up inside.

In this lesson, we’ll explore how to calculate the volume of common 3D solids like cuboids, cylinders, cones, spheres, and also tackle compound shapes made by combining two or more solids.

• 📦 Calculate volumes of basic solids like cubes and cylinders
• 🧊 Use formulas to find how much space is inside an object
• ⚙️ Break down compound shapes into simpler parts

🧠 Key Concepts and Volume Formulas

📐 Standard Volume Formulas

• Cuboid:
• Cube:
• Cylinder:
• Cone:
• Sphere:

🔁 Units of Volume

Always express volume in cubic units, such as:

• cm³ – cubic centimetres
• m³ – cubic metres
• L or ml – for liquids (1,000 cm³ = 1 L)

🔍 Worked Examples

1. 1. Volume of a cube: A cube has side length 4 cm.
      
      🟢 Volume is 64 cm³.

1. 1. Volume of a cylinder: Radius = 7 cm, height = 10 cm, use .
      
      🟢 Volume = 1540 cm³.

1. 1. Volume of a cone: Radius = 3 cm, height = 9 cm, use .
      
      🟢 Volume ≈ 84.78 cm³.

1. Volume of a compound shape: A water bottle is made of a cylinder (r = 4 cm, h = 10 cm) and a hemisphere (r = 4 cm). Use .
   Volume of cylinder = cm³
   Volume of hemisphere = cm³
   Total volume = cm³
   🟢 Total volume ≈ 636.37 cm³.

✍🏽 Practice Exercises

🅰️ Section A – Single Solids

1. Find the volume of a cuboid that is 6 m long, 3 m wide, and 2 m high.
2. A sphere has radius 5 cm. Use to find its volume.

🅱️ Section B – Compound Shapes

1. A container is made of a cone (r = 3 cm, h = 5 cm) on top of a cylinder (r = 3 cm, h = 10 cm). Find the total volume. Use .

✅ Answers and Explanations

• A1:
• A2:
• B1:
  • Cone volume:
  • Cylinder volume:
  • Total =

📌 Recap

• ✅ Volume measures how much space a 3D object takes up
• ✅ Use the correct formula depending on the shape
• ✅ Break compound shapes into smaller parts and add their volumes

💭 Reflection Prompt

Pick any container or bottle at home. Try estimating its volume using the shapes we’ve studied. Was it more or less than you expected? What formula helped you most?