Lesson 3: Surface Area of Solids

👨🏽‍🏫 Introduction

Ever wrapped a gift box and needed to know how much wrapping paper you’d need? Or painted a cylindrical water tank? That’s where surface area comes in! Surface area is the total area that covers the outside of a 3D object — like walls, covers, and labels.

In this lesson, we’ll learn how to calculate the surface area of different 3D solids, including cubes, cuboids, cylinders, cones, and spheres.

• 📦 Work with flat-faced solids like cubes and cuboids
• 🛢️ Explore curved shapes like cylinders and cones
• ⚽ Learn to calculate the outer covering of any solid object

🧠 Key Concepts and Surface Area Formulas

📐 Common Surface Area Formulas

• Cuboid:
• Cube:
• Cylinder: (2 circles + curved side)
• Cone: (base + slant surface)
• Sphere:

🎯 Notes:

• r = radius, h = height, l = slant height, s = side
• Use or as required
• Always express surface area in square units (cm², m², etc.)

🔍 Worked Examples

1. 1. Surface area of a cube: A cube has side length 5 cm.
      
      🟢 The total surface area is 150 cm².

1. 1. Surface area of a cuboid: A box is 4 m long, 3 m wide, and 2 m high.
      
      🟢 Surface area is 52 m².

1. 1. Surface area of a cylinder: Radius = 7 cm, height = 10 cm, use .
      
      
      🟢 Total surface area is 748 cm².

1. Surface area of a cone: Radius = 3 cm, slant height = 5 cm, use .
   
   🟢 Total surface area ≈ 75.36 cm².

✍🏽 Practice Exercises

🅰️ Section A – Cubes and Cuboids

1. Find the surface area of a cube with side 6 cm.
2. A cuboid has dimensions 5 m × 2 m × 3 m. Find its surface area.

🅱️ Section B – Cylinders and Cones

1. Find the surface area of a cylinder with radius 5 cm and height 8 cm. Use .
2. A cone has radius 4 cm and slant height 6 cm. Find its surface area using .

🅾️ Section C – Sphere

1. Find the surface area of a sphere with radius 10 cm.

✅ Answers and Explanations

• A1:
• A2:
• B1:
• B2:
• C1:

📌 Recap

• ✅ Surface area means the total area covering the outside of a 3D shape
• ✅ Each solid shape has a special surface area formula
• ✅ Always use square units like cm², m²

💭 Reflection Prompt

Look around your home — find any 3D object like a can, a box, or a football. Estimate its measurements and try to calculate its surface area. Were you surprised by how much material it would take to cover it?