EDEXCEL GCSE HIGHER MATHS - What is the Surface Area and Volume of Shapes

Edexcel GCSE Higher Maths - Surface Area and Volume of Shapes

Introduction

This tutorial will cover the concepts of surface area and volume for different 3D shapes, crucial for Edexcel GCSE Higher Maths.

Surface Area

Surface area is the total area of all the faces of a 3D shape. To calculate it, we need to find the area of each face and add them together.

Formulas:

• Cube: 6 * (side)^2
• Cuboid: 2 * (length * width + length * height + width * height)
• Cylinder: 2 * ? * radius * height + 2 * ? * (radius)^2
• Sphere: 4 * ? * (radius)^2
• Pyramid: Base area + (1/2) * perimeter of base * slant height
• Cone: ? * radius * slant height + ? * (radius)^2

Example:

Calculate the surface area of a cube with sides of 5cm.

• Solution: Surface area = 6 * (side)^2 = 6 * (5cm)^2 = 150 cm^2

Volume

Volume is the amount of space a 3D shape occupies. To calculate it, we need to multiply the area of the base by the height of the shape.

Formulas:

• Cube: (side)^3
• Cuboid: length * width * height
• Cylinder: ? * (radius)^2 * height
• Sphere: (4/3) * ? * (radius)^3
• Pyramid: (1/3) * base area * height
• Cone: (1/3) * ? * (radius)^2 * height

Example:

Calculate the volume of a cylinder with a radius of 3cm and a height of 10cm.

• Solution: Volume = ? * (radius)^2 * height = ? * (3cm)^2 * 10cm = 90? cm^3 ? 282.74 cm^3

Key Points

• Make sure you use the correct formula for the given shape.
• Pay attention to the units of measurement and ensure they are consistent throughout your calculations.
• Remember to include units in your final answer.
• Practice with various shapes and examples to solidify your understanding.

Practice Problems

1. Calculate the surface area and volume of a cuboid with dimensions of 6cm, 4cm, and 8cm.
2. Find the surface area of a sphere with a radius of 7cm.
3. Determine the volume of a cone with a radius of 5cm and a height of 12cm.

Conclusion

Understanding the concepts of surface area and volume is crucial for solving various problems in geometry. Practice with examples and formulas to excel in your Edexcel GCSE Higher Maths exam.