9.4.2. Cube

DO THIS Draw the pattern shown on a squared paper and cut it out [Fig 9.20(i)]. (You know that this pattern is a net of a cube. Fold it along the lines [Fig 9.20(ii)] and tape the edges to form a cube [Fig 9.20(iii)].

This activity involves creating a physical model of a cube using its net. A net is a two-dimensional representation of a 3D shape, which can be folded to form that shape. When you draw the net of a cube, you will notice that it consists of 6 square faces. When these squares are cut out and taped together, they create the cube, demonstrating how 3D objects can be constructed from 2D patterns.

Think of wrapping a gift. You lay out the wrapping paper (the net) flat and then fold it around the gift (the cube) to cover it completely. This shows how the 2D net becomes a 3D object.

(a) What is the length, width and height of the cube? Observe that all the faces of a cube are square in shape. This makes length, height and width of a cube equal (Fig 9.21(i)).

In a cube, all edges are of equal length, which means its length, width, and height are all the same. This property makes calculations easier since the area of each face will be the same, and it establishes that the cube is a regular polyhedron.

Consider a dice. Each side of a dice is a square and has the same dimensions. This means if you know one side's length, you can easily determine the size of the entire cube.

(b) Write the area of each of the faces. Are they equal? (c) Write the total surface area of this cube. (d) If each side of the cube is l, what will be the area of each face? (Fig 9.21(ii)). Can we say that the total surface area of a cube of side l is 6l² ?

Each face of the cube has an area that can be calculated by taking the side length (l) and squaring it (l²). Since a cube has 6 faces and all are identical, the total surface area can be found by multiplying the area of one face by 6. Therefore, the total surface area of a cube is given by the formula 6l².

Imagine painting a large cardboard box (a cube). If you were to paint each side completely, you'd have to paint 6 identical surfaces. Knowing the size of one side allows you to calculate the total paint needed for all six sides.

TRY THESE Find the surface area of cube A and lateral surface area of cube B (Fig 9.22).

In this exercise, students are asked to apply what they've learned about the surface area of a cube. To find the total surface area, they will need to use the previously established formula for surface area. Lateral surface area, which refers to the sides of the cube without the top and bottom, can be calculated separately and can be useful in real-world applications.

Think of a box of cereal; when painting the sides (lateral surface area) without covering the top or bottom, you need to consider only four out of the six sides, applying the same principles of surface area calculation in practical scenarios.

THINK, DISCUSS AND WRITE (i) Two cubes each with side b are joined to form a cuboid (Fig 9.23). What is the surface area of this cuboid? Is it 12b²? Is the surface area of cuboid formed by joining three such cubes, 18b²? Why?

This discussion encourages students to think critically about how combining shapes affects their surface area. When two cubes are joined to form a cuboid, certain faces are not exposed anymore, reducing the total surface area compared to the sum of the individual cubes' faces. An analysis of this allows for understanding the geometric properties of shapes when combined.

Imagine building with LEGO blocks. If two cubes are stacked, the surface area you can see (and thus paint or decorate) is less than if you had two separate cubes lying side by side because their bottom faces are touching and hidden from view.

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