Cubes and Cuboids are two of the most basic three-dimensional shapes, that we see around us everyday. A cube looks like a dice, with all sides equal, while a cuboid looks like a book or a box, with different lengths for each side. Understanding these shapes helps us calculate how much space they take up and how we can use them in real life.
What is a Cube?
A cube is a three-dimensional shape that consists of six equal square faces. It looks like a small box. Every corner of the cube has three edges meeting at right angles.
Properties of a Cube
Faces: 6 (all squares)
Edges: 12 (all equal in length)
Vertices: 8 (corners of the cube)
Volume of a Cube
The volume of a cube tells us how much space it takes up. A cube takes up space in three dimensions — length, width, and height. Since a cube has the same length on all sides, we can find the volume by multiplying the side length by itself three times (side x side x side). This is called “cubing” a number.
Formula
The volume of a cube is calculated using the formula:
( is the length of an edge)
Example
Imagine you have a cube with a side length of 2 cm. The cube has 2 cm in length, 2 cm in width, 2 cm in height. To find how much space it fills, you multiply these three numbers:
Volume = 2 × 2 × 2 = 8 cubic centimeters
This means the cube can hold 8 small cubes that are each 1 cm on all sides.
Let’s find the volume of a cube with a side length of 3 cm.
V = 3³ = 27 cm³
Surface Area of a Cube
The surface area of a cube is the total area of all its outer surfaces. It tells us how much space the outside of the shape covers. For example, if you wanted to wrap a cube in paper, the surface area is the amount of paper you’d need to cover the entire cube. Since a cube has six square faces, the surface area is just the total area of all six squares. To find the surface area of a cube, you first calculate the area of one face (which is a square) and then multiply it by 6 (because a cube has six faces).
Formula
The surface area of a cube is calculated using the formula:
Example:
If the side length of a cube is 3 cm, the area of a single square face of the cube is 3×3 = 9 square centimeters. The surface area is the total of the areas of all six faces. Surface Area = 6×9 = 54 square centimeters.
This means that if you were to unfold the cube and lay all the squares flat, the total area covered by the cube would be 54 square centimeters.
Let’s find the surface area of a cube with the length of its edge as 2 cm.
SA = 6a
What is a Cuboid?
A cuboid is a three-dimensional shape with six rectangular faces. It looks like a box, a book, or a brick. The opposite sides of a cuboid are always the same size, but not all sides have to be equal like in a cube.
Properties of a Cuboid
Faces: 6 (all rectangles)
Edges: 12 (edges can be of different lengths)
Vertices: 8 (corners of the cuboid)
Volume of a Cuboid
The volume of a cuboid tells us how much space it occupies or how much it can hold inside. Think of it as stacking layers of rectangles, one on top of the other, to fill up the entire cuboid. The area of each rectangular layer is l x b, and a total of h rectangles should be stacked to fill up the cuboid. To calculate the volume, we multiply the cuboid’s length, width, and height.
Length: The distance from one end of the cuboid to the other (along one edge).
Breadth: How wide the cuboid is from that edge to the opposite edge.
Height: How tall the cuboid is from top to bottom.
Example
A cuboid has Length = 6 cm, Width = 4 cm, Height = 3 cm.
To find the volume, we multiply these three numbers:
Surface Area of a Cuboid
The surface area of a cuboid tells us how much total space all six faces of the cuboid cover. Each face of a cuboid is a rectangle, and opposite faces are the same size. To calculate the surface area, we need to find the area of each pair of faces and then add them up.
Let’s say a cuboid has Length = 6 cm, Breadth = 4 cm, Height = 3 cm.
We can calculate the surface area step by step:
- Find the area of the top and bottom faces. (length × breadth): 6×4 = 24cm
- Since there are two such faces:
- Find the area of the front and back faces. (length × height):
- Since there are two such faces:
- Find the area of the side faces (breadth × height): 4×3 = 12cm
- Since there are two such faces:
- Finally, add up all the areas:
- So, the total surface area of the cuboid is 108 cm².
Surface Area = 2x(lengthxbreadth) + 2x(lengthxheight) + 2x(breadthxheight)
Formula
The surface area of a cuboid is calculated using the formula:
Example
A cuboid has length 8 cm, breadth 5 cm and height 2 cm.
Surface Area = 2(8×5 + 5×2 + 8×2) = 2(40+10+16) = 2×66 = 132 cm²
Points to Remember
Volume tells us how much space is inside the cuboid.
Surface area tells us how much space is covered by the outer surface of the cuboid.
The volume is measured in cubic units (like cm³ or m³), while surface area is measured in square units (like cm² or m²).
Real-World Examples of Cubes and Cuboids
In our everyday lives, we come across many examples of cubes and cuboids. Cubes can be seen in objects like dice, Rubik’s cubes, and sugar cubes, where all the edges are equal with square faces. On the other hand, cuboids are more common in things like shoeboxes, books, bricks, and refrigerators. These objects have rectangular faces with different lengths, widths, and heights. While both shapes are similar in having six faces, cubes have all equal sides, and cuboids have varying dimensions.
Fun Facts about Cubes and Cuboids
Cubes in Nature: Did you know that some minerals naturally form cubes? One example is salt! If you look closely at salt crystals, they are tiny cubes.
Cube’s Symmetry: A cube has perfect symmetry. You can slice it through the middle from different angles, and each part will look exactly the same!
A Rubik’s Cube: The popular puzzle, the Rubik’s Cube, is based on the shape of a cube. There are 43 quintillion ways to arrange the squares on a Rubik’s Cube, but only one correct solution!
Cuboids Everywhere: Look around your classroom or home — books, boxes, and even your phone are shaped like cuboids. We use cuboids all the time without realizing it!
Volume of a Cube: If you stack 1 cm cubes to form a bigger cube with sides of 10 cm, it would take exactly 1,000 small cubes to fill it up. That’s why volume is measured in cubic units!
Packing Efficiency: Cuboids are great for packing because their shape makes it easy to stack without leaving any gaps. That’s why most shipping boxes are cuboid-shaped.
Practice Quiz on Cubes and cuboids
FAQs on Cubes and Cuboids
- A square prism has two square bases and four rectangular faces. It can have different lengths for the height (side connecting the bases) and the side lengths of the square bases.
- A cube is a special type of square prism where all sides are equal—all faces are squares of the same size.
- A cube is a three-dimensional extension of a square. A square is a two-dimensional shape with equal sides, and a cube is formed by extending a square into three dimensions.
- A cube has a smaller surface area compared to a cuboid with the same volume. This is because, in a cube, all sides are equal, minimising the surface area for a given volume.