EDEXCEL GCSE FOUNDATION MATHS - What is Surface Area

Edexcel GCSE Foundation Maths: What is Surface Area?

Introduction

Surface area is the total area of all the faces of a 3D shape. Imagine you were to wrap a gift, the amount of wrapping paper needed would be the surface area of the gift box.

Understanding Surface Area

• Faces: A face is a flat surface of a 3D shape. A cube has 6 square faces, a rectangular prism has 6 rectangular faces, and a pyramid has one base and several triangular faces.
• Area: The area of a flat shape is the amount of space it covers. We measure area in square units, like square centimeters (cm²) or square meters (m²).

Calculating Surface Area

To calculate the surface area of a shape, we need to find the area of each individual face and then add them together.

Example: Calculating the Surface Area of a Cube

Let's say we have a cube with sides of length 5cm.

1. Area of one face: The area of a square is side * side, so the area of one face is 5cm * 5cm = 25cm².
2. Total surface area: A cube has 6 faces, so the total surface area is 6 * 25cm² = 150cm².

Formulae for Common Shapes

Here are some formulae for calculating the surface area of common shapes:

• Cube: Surface area = 6 * side²
• Cuboid: Surface area = 2(length * width) + 2(length * height) + 2(width * height)
• Cylinder: Surface area = 2?r² + 2?rh (where r is the radius and h is the height)
• Sphere: Surface area = 4?r² (where r is the radius)

Example: Calculating the Surface Area of a Cylinder

Let's say we have a cylinder with a radius of 3cm and a height of 10cm.

1. Area of the top and bottom circles: Area = ?r² = ? * 3cm * 3cm ? 28.27cm²
2. Area of the curved surface: Area = 2?rh = 2 * ? * 3cm * 10cm ? 188.50cm²
3. Total surface area: 28.27cm² + 28.27cm² + 188.50cm² ? 245.04cm²

Tips for Success

• Visualize: Draw a diagram of the shape to help you understand the faces.
• Break it down: Divide the shape into simpler shapes if needed (like a rectangular prism into squares and rectangles).
• Use the correct formula: Make sure you are using the right formula for the shape you are working with.
• Be careful with units: Always remember to include the correct units for your answer (e.g., cm², m²).

Practice makes perfect! Solve lots of practice problems to solidify your understanding of surface area.