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171 LearnersLast updated on August 5, 2025
Surface Area of Composite Shapes
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.
What is 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.
Surface Area of Composite Shapes Formula
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.
Calculating Surface Area of Composite Shapes
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.
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Example Calculations of Surface Area
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.
Volume of Composite Shapes
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.
Ignoring Overlapping Areas
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.
Mistake 1
Misidentifying Component Shapes
Misidentifying the basic shapes that make up the composite shape can lead to incorrect calculations. Make sure to clearly identify each component shape and use the correct formulas.
Mistake 2
Using Inaccurate Formulas
Using incorrect formulas for the component shapes is a common error. Always double-check the formulas for each shape involved in the composite shape calculation.
Mistake 3
Forgetting to Add All Surfaces
Students may forget to include all relevant surfaces, especially when a shape has more than one part. Ensure that every visible and relevant surface is included in the calculations.
Mistake 4
Confusing Volume and Surface Area
Some students confuse volume calculations with surface area calculations. Remember that volume measures space inside a shape, while surface area measures the outer surface.
Mistake 5
Solved Examples of Surface Area of Composite Shapes
Find the surface area of a composite shape consisting of a rectangular prism with dimensions 8 cm by 5 cm by 3 cm and a cylinder with radius 2 cm and height 5 cm attached to one face.
Total Surface Area = 196.72 cmยฒ
Problem 1
Calculate the surface area of the rectangular prism: SA = 2(lw + lh + wh) = 2(8ร5 + 8ร3 + 5ร3) = 2(40 + 24 + 15) = 158 cmยฒ. Calculate the surface area of the cylinder: SA = 2ฯr(h + r) = 2ร3.14ร2(5 + 2) = 87.92 cmยฒ. Subtract the overlapping area: Overlap = ฯrยฒ = 3.14ร2ยฒ = 12.56 cmยฒ. Total Surface Area = 158 + 87.92 - 12.56 = 196.72 cmยฒ.
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.
Explanation
Total Surface Area = 402.88 cm²
Problem 2
Calculate the surface area of the cylinder (excluding the top base): SA = 2ฯrh = 2ร3.14ร4ร10 = 251.2 cmยฒ. Calculate the surface area of the sphere: SA = 4ฯrยฒ = 4ร3.14ร4ยฒ = 200.96 cmยฒ. Total Surface Area = 251.2 + 200.96 = 402.88 cmยฒ.
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.
Explanation
Total Surface Area = 275.5 cm²
Problem 3
Calculate the surface area of the cube: SA = 6aยฒ = 6ร5ยฒ = 150 cmยฒ. Calculate the surface area of the hemisphere (excluding the base): SA = 2ฯrยฒ = 2ร3.14ร5ยฒ = 157 cmยฒ. Subtract the area of the base of the hemisphere: Overlap = ฯrยฒ = 3.14ร5ยฒ = 78.5 cmยฒ. Total Surface Area = 150 + 157 - 78.5 = 275.5 cmยฒ.
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.
Explanation
Total Surface Area = 201.06 cm²
Problem 4
Calculate the surface area of the cone (excluding the base): SA = ฯrl = 3.14ร3ร5 = 47.1 cmยฒ, where l is the slant height found using lยฒ = rยฒ + hยฒ = 3ยฒ + 4ยฒ = 25, l = 5. Calculate the surface area of the cylinder: SA = 2ฯrh + ฯrยฒ = 2ร3.14ร3ร6 + 3.14ร3ยฒ = 113.04 + 28.26 = 141.3 cmยฒ. Total Surface Area = 47.1 + 141.3 - 28.26 = 160.14 cmยฒ.
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.
Explanation
Total Surface Area = 144 cm²
It is the total area that covers the outer surfaces of the composite shape, including all its component parts.
1.How do you find the surface area of a composite shape?
2.What is the difference between volume and surface area?
3.Can composite shapes include 2D shapes?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of Composite Shapes
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.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
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