The lateral surface of a cone is a sector. Use the formula for the surface area of a sphere.
Surface area of a cone = πr² + πrl（r: radius of the base, l: slant height）
Surface area of a sphere = 4πr²
📘 Example ①
Find the surface area of a cone with a base radius of 3 cm and a slant height of 5 cm.
Answer: Area of base = π×3² = 9π. Lateral surface area = π×3×5 = 15π.
Surface area = 9π + 15π = 24π cm²
Find the surface area of a cone with a base radius of 3 cm and a slant height of 5 cm.
Answer: Area of base = π×3² = 9π. Lateral surface area = π×3×5 = 15π.
Surface area = 9π + 15π = 24π cm²
📘 Example ②
Find the surface area of a sphere with a radius of 6 cm.
Answer: 4π×6² = 4π×36 = 144π cm²
Find the surface area of a sphere with a radius of 6 cm.
Answer: 4π×6² = 4π×36 = 144π cm²
💡 Key Points
- Cone: base (πr²) + lateral surface (πrl)
- Sphere: 4πr²
- The slant height (l) is the length from the vertex to a point on the circumference of the base
Practice Problems
- Find the surface area of a cone with a base radius of 4 cm and a slant height of 7 cm (leave π as it is).
- Find the surface area of a sphere with a radius of 3 cm (leave π as it is).
Answers and Explanations
- Answer: 44π cm². Base=16π, lateral surface=28π, total=44π.
- Answer: 36π cm². 4π×9=36π.