Lesson 2: Basic Solids – Properties of Cubes, Cuboids, Cylinders

📘 Introduction

Every day, you interact with solid shapes — a box of cereal (cuboid), a football (sphere), or a can of milk (cylinder). These shapes are called solids or 3D shapes because they have length, width, and height.

In this lesson, we’ll explore the common types of solids, their properties, and how to calculate surface area and volume where needed.

Let’s build your geometric thinking from solid ground!

🧠 Key Concepts and Explanations

1. What Are Solids?

Solids are 3-dimensional (3D) shapes. Unlike flat 2D shapes (like squares or circles), solids have:

• Faces: Flat or curved surfaces
• Edges: Where two faces meet
• Vertices: Corner points

2. Types of Common Solids

Note: While a cube and cuboid look similar, all sides of a cube are equal, but in a cuboid, the sides can be different.

3. Surface Area and Volume

Surface area is the total area covering the surface of the solid.
Volume is the amount of space a solid occupies.

Solid	Surface Area Formula	Volume Formula
Cube
Cuboid
Cylinder

🧮 Sample Problem Walkthroughs

Example 1: A cube has a side length of 4 cm. Find its surface area and volume.

Surface Area = =

Volume =

Example 2: A cylinder has radius 3 cm and height 5 cm. Find its volume.

Volume =

Example 3: A cuboid has dimensions 6 cm by 4 cm by 3 cm. Find its surface area.

Surface Area =

✏️ Practice Exercises

Section A: Naming and Properties

1. List the number of faces, edges, and vertices of a cone.
2. Which solid has no edges or vertices?
3. Give two real-life examples each of a cuboid and a cylinder.

Section B: Calculations

4. A cube has side length 5 cm. Find its surface area and volume.
5. A cuboid has dimensions 7 cm, 3 cm, and 2 cm. Find its volume.
6. A cylinder has radius 2.5 cm and height 10 cm. Calculate its surface area (use π = 3.14).

📝 Answers & Explanations

• Q1: Cone has 2 faces, 1 edge, 1 vertex
• Q2: Sphere
• Q3: Cuboid: TV, shoebox; Cylinder: drum, pipe
• Q4: SA = 150 cm², V = 125 cm³
• Q5: V = 7 × 3 × 2 = 42 cm³
• Q6: SA =

🔁 Recap

• Solids are 3D shapes with faces, edges, and vertices
• Common solids include cubes, cuboids, cylinders, cones, and spheres
• Surface area and volume help us describe size and space
• Each solid has specific properties and formulas

🪞Reflection Prompt

Think about your home or classroom. How many different solid shapes can you find? Can you estimate their volumes or surface areas?