Boxes and Sketches: CBSE Class 5 Maths Chapter 9 Guide

What are Nets? From 2D to 3D

Imagine you have a cube-shaped gift box. If you carefully cut along some of its edges and lay it completely flat, the 2D shape you get is the 'net' of the cube. A net is a flat pattern that shows all the faces of a 3D object connected together. When you fold this net along the edges, you can remake the original 3D shape. Think of it as a secret code or a blueprint for a box! But be careful, not just any arrangement will work. For a cube, you need exactly 6 squares, but they must be positioned so they can fold up perfectly without any gaps or overlapping faces. Learning about nets is like gaining a superpower to see the connection between the flat world of drawings (2D) and the solid world of objects (3D).

How to Check if a Net Can Form a Cube

1. Step 1: Count the Faces — A cube always has 6 square faces. Your first check is to count the squares in the net. If there are not exactly 6 squares, it cannot form a closed cube. If there are 5, it might form an open box, but not a closed one.
2. Step 2: Choose a Base — Look at the net and pick one square to be the bottom of your cube. It's often easiest to choose one in the middle of the arrangement. Imagine placing this square flat on a table.
3. Step 3: Imagine Folding the Sides — Now, in your mind, fold up all the squares that are directly attached to the edges of your base square. These will become the four 'walls' or side faces of the cube.
4. Step 4: Check for a Top and Overlaps — Finally, look for the last remaining square. Will it fold over to become the 'lid' or top of the cube? A correct net will have one face that perfectly covers the top. If two faces try to cover the top (overlap) or if one side is left open, the net will not work.

Visualizing with Deep Drawings

• A 'deep drawing' (also called an oblique sketch) is a simple way to make a shape on paper look 3D. Let's see how to draw a cube:
• Step 1: Draw a square. This will be the front face of your cube.
• Step 2: From three of the corners (for example, the top-right, bottom-right, and bottom-left), draw short, parallel lines slanting away. These lines create the illusion of depth.
• Step 3: Connect the ends of these slanted lines to form another square. This will be the back face of your cube.
• You have now drawn a cube that looks solid! This technique helps us show the length, width, and height of an object on a flat surface.

Key Things to Remember

• Not All 6-Square Shapes Work: Just because a net has 6 squares doesn't mean it will fold into a cube. The arrangement of the squares is very important.
• Opposite Faces on a Dice: On a standard dice, the numbers on opposite faces always add up to 7. So, 1 is opposite 6, 2 is opposite 5, and 3 is opposite 4.
• Open vs. Closed Boxes: An open box (a box without a lid) is made from a net with 5 faces. A closed box needs a net with 6 faces.
• 3D Objects have Dimensions: 3D shapes like boxes have length, width, and height. 2D shapes like squares only have length and width.

Practice Questions with Solutions

• Q: You are given a net made of 6 squares in a straight line. Will this net fold to make a cube? A: Step 1: Imagine choosing one square as the base. Step 2: Fold the squares on either side of the base to make the walls. You will have a long strip of four walls. Step 3: The last square will overlap with one of the other squares instead of forming a top. There will be no face to form the top of the cube. Final answer: No, a net of 6 squares in a single straight line will not form a cube.
• Q: A standard dice is rolled. If the number 2 is on the top face, what number is on the bottom face? A: Step 1: Recall the rule for a standard dice. The numbers on opposite faces always add up to 7. Step 2: We are given that the top face is 2. Let the bottom face be 'x'. Step 3: According to the rule, 2 + x = 7. Step 4: To find x, we calculate 7 - 2 = 5. Final answer: The number on the bottom face will be 5.
• Q: How would you draw a deep drawing of a matchbox (a cuboid)? A: Step 1: Start by drawing a rectangle. This is the front face of the matchbox. Step 2: From the top right, bottom right, and top left corners of the rectangle, draw short, parallel lines slanting backwards and upwards. Step 3: Connect the ends of these slanted lines. This will form the back face of the matchbox, creating a 3D effect. Final answer: By following these steps, you create a drawing that looks like a solid matchbox, showing its length, height, and breadth.
• Q: You have a flat shape made of 5 squares arranged like a plus sign ('+'). Can this be folded into an open box? A: Step 1: Imagine the central square as the base of the open box. Step 2: Imagine folding up the four squares that stick out from the center. Each of these four squares will form one of the four sides or walls of the box. Step 3: Since there is no sixth square, the top is left open. Final answer: Yes, this net will fold perfectly to create an open box (a box without a lid).

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