EDEXCEL GCSE FOUNDATION MATHS - What is the Surface Area of a Sphere or Cone

Edexcel GCSE Foundation Maths: Surface Area of a Sphere and Cone

1. Surface Area of a Sphere

Formula:

Surface Area = 4?r²

Where:

• r represents the radius of the sphere

Example:

Calculate the surface area of a sphere with a radius of 5cm.

• Substitute r = 5cm into the formula: Surface Area = 4?(5cm)²
• Calculate: Surface Area = 4?(25cm²) Surface Area = 100? cm² Surface Area ? 314.16 cm² (using ? ? 3.14)

Key Points:

• The surface area of a sphere is the total area of its curved surface.
• Always remember to use the correct units (cm², m², etc.) in your answer.
• If you are given the diameter of the sphere, remember to divide it by 2 to find the radius.

2. Surface Area of a Cone

Formula:

Surface Area = ?r² + ?rl

Where:

• r represents the radius of the base of the cone
• l represents the slant height of the cone (the distance from the tip of the cone to a point on the edge of the base)

Example:

Calculate the surface area of a cone with a radius of 4cm and a slant height of 7cm.

• Substitute r = 4cm and l = 7cm into the formula: Surface Area = ?(4cm)² + ?(4cm)(7cm)
• Calculate: Surface Area = 16? cm² + 28? cm² Surface Area = 44? cm² Surface Area ? 138.23 cm² (using ? ? 3.14)

Key Points:

• The surface area of a cone includes the area of the circular base and the curved surface.
• You will often need to use Pythagoras' theorem to calculate the slant height (l) if it is not given directly.

Summary

Understanding the formulas for the surface area of a sphere and a cone is essential for solving various problems in geometry. Remember to use the correct formulas and units, and be sure to practice solving examples to solidify your understanding.