Last updated on August 5th, 2025
Composite shapes are shapes that are made up of two or more simple geometric shapes. The surface area of a composite shape is the total area covered by its outer surfaces. In this article, we will learn about the surface area of composite shapes.
The surface area of a composite shape is the total area occupied by the boundary or surface of the combined shapes. It is measured in square units. Composite shapes are formed by joining two or more simple shapes like rectangles, triangles, circles, cylinders, cones, etc.
To find the surface area of a composite shape, we calculate the surface area of each individual shape and then combine them, taking into account any overlapping areas.
Composite shapes can be made from various basic shapes, such as prisms, cylinders, cones, and spheres.
To find the surface area of a composite shape, we calculate the surface area of each component shape separately and then add or subtract these areas, depending on how the shapes are combined.
For example, if two shapes are joined without overlapping, their areas are added together.
The method for calculating the surface area of composite shapes involves breaking down the complex shape into simpler parts.
Find the surface area of each part separately using their respective formulas and then sum them up. Ensure to subtract any overlapping areas.
For instance, if a cylindrical shape is attached to a cuboid, calculate the surface areas of both and combine them.
To illustrate the calculation of the surface area of composite shapes, consider a shape consisting of a cylinder with a hemisphere on top.
Calculate the surface area of the cylinder and the hemisphere separately, then add them together, ensuring not to double-count any shared areas.
The volume of a composite shape shows how much space is inside it.
To find the volume of a composite shape, calculate the volume of each individual shape separately and then sum them up, making sure to account for any shared or overlapping regions.
Students often forget to subtract the areas where two shapes overlap. Always ensure to account for any shared regions so that they are not counted twice.
Calculate the surface area of the rectangular prism: SA = 2(lw + lh + wh) = 2(8×5 + 8×3 + 5×3) = 2(40 + 24 + 15) = 158 cm². Calculate the surface area of the cylinder: SA = 2πr(h + r) = 2×3.14×2(5 + 2) = 87.92 cm². Subtract the overlapping area: Overlap = πr² = 3.14×2² = 12.56 cm². Total Surface Area = 158 + 87.92 - 12.56 = 196.72 cm².
Find the surface area of a composite shape consisting of a sphere with radius 4 cm placed on top of a cylinder with radius 4 cm and height 10 cm.
Total Surface Area = 402.88 cm²
Calculate the surface area of the cylinder (excluding the top base): SA = 2πrh = 2×3.14×4×10 = 251.2 cm². Calculate the surface area of the sphere: SA = 4πr² = 4×3.14×4² = 200.96 cm². Total Surface Area = 251.2 + 200.96 = 402.88 cm².
A composite shape consists of a cube with side 5 cm and a hemisphere with radius 5 cm on top. Find the total surface area.
Total Surface Area = 275.5 cm²
Calculate the surface area of the cube: SA = 6a² = 6×5² = 150 cm². Calculate the surface area of the hemisphere (excluding the base): SA = 2πr² = 2×3.14×5² = 157 cm². Subtract the area of the base of the hemisphere: Overlap = πr² = 3.14×5² = 78.5 cm². Total Surface Area = 150 + 157 - 78.5 = 275.5 cm².
Find the surface area of a composite shape made of a cone with base radius 3 cm and height 4 cm, and a cylinder with the same radius and height 6 cm.
Total Surface Area = 201.06 cm²
Calculate the surface area of the cone (excluding the base): SA = πrl = 3.14×3×5 = 47.1 cm², where l is the slant height found using l² = r² + h² = 3² + 4² = 25, l = 5. Calculate the surface area of the cylinder: SA = 2πrh + πr² = 2×3.14×3×6 + 3.14×3² = 113.04 + 28.26 = 141.3 cm². Total Surface Area = 47.1 + 141.3 - 28.26 = 160.14 cm².
A composite shape consists of a pyramid with a square base of side 4 cm and height 6 cm, placed on top of a cube with side 4 cm. Find the total surface area.
Total Surface Area = 144 cm²
Students often make mistakes while calculating the surface area of composite shapes, which leads to incorrect answers. Below are some common mistakes and the ways to avoid them.
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