Find the surface area of a solid made by combining multiple solids. Note that surfaces in contact are not included in the surface area.
📘 Example ①
Find the surface area of a composite solid formed by placing a cone with the same base on top of a cylinder with a base radius of 3 cm (slant height of the cone: 5 cm; height of the cylinder: 4 cm).
Answer: Bottom base of the cylinder = π×9 = 9π.
Lateral surface of the cylinder = 2π×3×4 = 24π.
Lateral surface of the cone = π×3×5 = 15π.
(Do not include the surfaces in contact: the top of the cylinder and the base of the cone.)
Surface area = 9π + 24π + 15π = 48π cm²
Find the surface area of a composite solid formed by placing a cone with the same base on top of a cylinder with a base radius of 3 cm (slant height of the cone: 5 cm; height of the cylinder: 4 cm).
Answer: Bottom base of the cylinder = π×9 = 9π.
Lateral surface of the cylinder = 2π×3×4 = 24π.
Lateral surface of the cone = π×3×5 = 15π.
(Do not include the surfaces in contact: the top of the cylinder and the base of the cone.)
Surface area = 9π + 24π + 15π = 48π cm²
💡 Key Point
- Do not include the surfaces at the joint in the surface area
- Calculate only the surfaces on the outside
Practice Problems
- Find the surface area of a composite solid formed by placing a regular square pyramid with the same base on top of a square prism whose base is a square with side length 4 cm and whose height is 5 cm (slant height: 3 cm).
Answer and Explanation
- Answer: Bottom base 16 + lateral surface of the square prism 4×4×5=80 + lateral surface of the square pyramid (1/2)×4×3×4=24 = 120 cm². The top base at the joint is not included.