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107 LearnersLast updated on August 30, 2025
Surface Area of 3D Figures
Understanding the surface area of 3D figures is crucial in geometry. Surface area refers to the total area that the surface of an object occupies. Different 3D figures have unique formulas for calculating their surface areas. In this article, we will explore the surface area of various 3D figures.
What is the Surface Area of a 3D Figure?
The surface area of a 3D figure is the total area covered by the outer surfaces of the shape.
It is measured in square units. 3D figures are solid shapes that have three dimensions: length, width, and height. These include shapes like cubes, spheres, cylinders, cones, and pyramids.
Each shape has a unique formula for calculating its surface area based on its geometric properties.
Surface Area Formulas for Common 3D Figures
Common 3D figures include spheres, cylinders, cubes, cones, and pyramids, each with specific formulas to determine their surface areas.
Understanding these formulas helps in solving practical problems involving these shapes.
Surface Area of a Sphere
The surface area of a sphere is the total area covered by its outer surface. It is calculated using the formula: Surface Area = 4πr², where r is the radius of the sphere.
Surface Area of a Cylinder
A cylinder has two circular bases and a curved surface in between.
The surface area is calculated as the sum of the areas of these three surfaces using the formula:
Surface Area = 2πrh + 2πr²,
where r is the base radius and h is the height of the cylinder.
Surface Area of a Cube
The surface area of a cube is the total area of all six identical square faces. It is calculated using the formula:
Surface Area = 6a², where a is the length of a side of the cube.
Surface Area of a Pyramid
A pyramid has a polygonal base and triangular faces that meet at a point called the apex.
The surface area is calculated by adding the base area to the sum of the areas of the triangular faces.
The formula depends on the shape of the base and the height of the triangular faces.
Confusion Between Different 3D Shapes
Students sometimes confuse the formulas for different shapes, leading to errors. Be sure to understand which formula applies to which shape and double-check that you’re using the correct one.
Mistake 1
Misidentifying the Shape's Dimensions
Another common mistake is using the wrong dimensions in the formula. Ensure you correctly identify the radius, height, or side length as required by the formula for the specific shape.
Mistake 2
Inaccurate Use of π
Using incorrect values for π can lead to wrong answers.
Use π as 3.14 or 22/7 for calculations unless otherwise specified.
Mistake 3
Neglecting Units of Measurement
Sometimes, students forget to include units in their answers or mix different units.
Always ensure that the units are consistent and include them in the final answer.
Mistake 4
Forgetting to Add All Faces or Surfaces
When calculating the surface area of shapes like pyramids or cylinders, students often forget to include all parts of the shape. Ensure you account for all faces or surfaces in your calculations.
Mistake 5
Solved Examples of Surface Area of 3D Figures
Find the surface area of a sphere with a radius of 5 cm.
Surface Area = 314 cm²
Problem 1
Given r = 5 cm. Use the formula: Surface Area = 4πr² = 4 × 3.14 × 5² = 4 × 3.14 × 25 = 314 cm²
Calculate the surface area of a cylinder with a radius of 3 cm and a height of 7 cm.
Explanation
Surface Area = 188.4 cm²
Problem 2
Use the formula: Surface Area = 2πrh + 2πr² = 2 × 3.14 × 3 × 7 + 2 × 3.14 × 3² = 131.88 + 56.52 = 188.4 cm²
Find the surface area of a cube with side length 4 cm.
Explanation
Surface Area = 96 cm²
Problem 3
Use the formula: Surface Area = 6a² = 6 × 4² = 6 × 16 = 96 cm²
Determine the surface area of a cone with a radius of 2 cm and a slant height of 5 cm.
Explanation
Surface Area = 44 cm²
Problem 4
Surface Area = πr(r + l) = 3.14 × 2 × (2 + 5) = 3.14 × 2 × 7 = 44 cm²
A pyramid has a square base with a side length of 3 cm and a slant height of 4 cm. Find its surface area.
Explanation
Surface Area = 33 cm²
Surface area is the total area covered by the outer surfaces of a 3D figure.
1.How do you calculate the surface area of a sphere?
2.What is the difference between a cube and a cuboid?
3.Is the surface area of a cone the same as that of a cylinder?
4.What units are used for surface area?
Common Mistakes and How to Avoid Them in Calculating Surface Areas of 3D Figures
Many students make mistakes when calculating the surface area of 3D figures, which can lead to incorrect results. Here are some common mistakes and tips to avoid them.
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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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: She has songs for each table which helps her to remember the tables
