Last updated on July 30th, 2025
A cube and a cuboid are 3-dimensional shapes with flat surfaces. The surface area of these shapes is the total area covered by their outer surfaces. In this article, we will learn about the surface area of a cube and a cuboid.
The surface area of a cube and a cuboid is the total area occupied by their boundaries or surfaces. It is measured in square units.
A cube is a 3D shape with six equal square faces, while a cuboid has six rectangular faces. Both shapes have a total surface area, which is the sum of the areas of all their faces.
Both a cube and a cuboid have six faces, and their surface areas are calculated by summing the areas of all these faces. Below are the formulas for calculating their surface areas.
For a cube: Total Surface Area (TSA) = 6a² Here, a is the length of a side of the cube.
For a cuboid: Total Surface Area (TSA) = 2(lb + bh + hl) Where l is the length, b is the breadth, and h is the height of the cuboid.
The surface area of a cube is the total area of all six identical square faces. The formula to calculate the surface area of a cube is:
Surface Area = 6a² square units
Here, a is the side length of the cube.
The surface area of a cuboid is the sum of the areas of all its rectangular faces. The formula to calculate the surface area of a cuboid is:
Surface Area = 2(lb + bh + hl) square units
Where l is the length, b is the breadth, and h is the height of the cuboid.
The volume of a cube is the space it occupies, calculated as: Volume of a cube = a³ cubic units
The volume of a cuboid is the space it occupies, calculated as: Volume of a cuboid = l × b × h cubic units
Students sometimes confuse the side length of a cube with the edge length of a cuboid. Remember, in a cube, all edges are equal, while a cuboid has different edge lengths.
Given a = 4 cm. Use the formula: Surface Area = 6a² = 6 × 4² = 6 × 16 = 96 cm²
Find the total surface area of a cuboid with length 5 cm, breadth 3 cm, and height 2 cm.
TSA = 62 cm²
Use the formula: TSA = 2(lb + bh + hl) = 2(5 × 3 + 3 × 2 + 2 × 5) = 2(15 + 6 + 10) = 2 × 31 = 62 cm²
A cube has a side of 7 cm. Find the total surface area.
Surface Area = 294 cm²
Use the formula: Surface Area = 6a² = 6 × 7² = 6 × 49 = 294 cm²
Find the surface area of a cuboid with dimensions 6 cm by 4 cm by 3 cm.
TSA = 108 cm²
TSA = 2(lb + bh + hl) = 2(6 × 4 + 4 × 3 + 3 × 6) = 2(24 + 12 + 18) = 2 × 54 = 108 cm²
The surface area of a cube is 150 cm². Find the side length.
Side length = 5 cm
Students often make mistakes while calculating the surface area of a cube and a cuboid, leading to incorrect answers. Below are some common mistakes and ways to avoid them.
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