Boxes and Sketches Class 5 Notes Maths Chapter 9

2D Shapes

• 2D means two-dimensional, like having width and height.
• Shapes in 2D are flat, like a piece of paper.
• Examples include rectangles and circles; they don't have depth.
• Dimensions are like measurements in different directions.
• In 2D, we talk about length, and width (or breadth), but no depth or height.
• 2D objects can't be physically held; they're just flat on a surface.

3D Shapes

Properties of 2D Shapes

Circle

• A circle is a 2D closed shape with no sides or edges made out of a curved line. 
• A circle is made up of several different pieces, such as radius, diameter, and circumference.
• Examples include Coins, wheels, and pizzas.
  
  Circle

Triangle

• .A triangle is a closed shape that has three sides, three vertices, and three angles.
• It is a polygon with inner angles summing 180 degrees.
  
  Triangle

Square

• A square is a two-dimensional form having four equal sides and each angle equal to 90 degrees. 
• Examples include a loaf of bread and a chessboard.
  
  Square

Rectangle

• A rectangle is a two-dimensional object having four sides that are equal and parallel, and all four angles measure 90 degrees. 
• Examples include Tabletops, blackboards, and cardboard.
  
  Rectangle

Properties of 3D Shapes

Sphere 

• A sphere has only one curved surface.
• For example, planets, balls, globes, etc.
  
  Sphere 

Hemisphere    

• A hemisphere has a single face, one curved surface, and one edge.

• For example, a scoop of ice cream, cups, etc.
  Hemisphere    

Cone

• A cone has a single face, one curved surface, one edge, and one vertex.
• For example, ice cream cones, traffic cones, etc.
  Cone

Cube

• A cube is a solid three-dimensional object. It has six faces, twelve edges, and eight vertices.
• For example, ice cubes, gift boxes, etc.
  Cube

Cylinder

• A cylinder is made up of two faces, one curved surface, and two edges.
• For example, battery, test tube, etc.
  Cylinder

Solved Examples of 2D and 3D Shapes

Example 2: Which of the following is a 3D shape?
  Cone, Square, Sphere, Cuboid, Cylinder, Parallelogram
Solution: Cone, Sphere,  Cuboid, Cylinder.

Example 3: State whether the following are true or false.
(a) A three-dimensional shape has 3 dimensions.
(b) Three-dimensional shapes are also called flat shapes.
(c) Three-dimensional shapes occupy space.
(d) All three-dimensional shapes have flat faces.
Sol: (a)True
(b) False. Three-dimensional shapes are also called solid shapes.
(c) True
(d) False. The sphere is a three-dimensional shape with no flat face.

2D Shapes vs 3D Shapes

2D to 3D shape

• A net is like a flat paper plan that shows how a 3D shape looks when you unfold it.
• Imagine it's like a pattern you use to make a paper model of a 3D figure.
• Think of a box. It's a solid 3D object shaped like a rectangular block.
• Other shapes have their own nets too, like puzzles to make different 3D shapes.
  

Floor Maps

• The floor map is like a picture of a house.
• It shows where the doors and windows are in the house.
• The front side of the house is where the door is.
  
• On the front side, there are two windows.
• We can't see how big the house is or how tall the windows are from the floor map.

Deep Drawings

• A deep drawing of a home is a special way of drawing that shows how long, wide, and tall the house is.
• It's like making the house look real in a picture.
• This kind of drawing is called a 3D depiction of a house map.
• Below is an example of a deep drawing of the given floor map.

Deep Drawing of a Cube and Cuboid

• Cuboid: A cuboid is a three-dimensional (3D) object with six faces. A cuboid has variable lengths, widths, and heights. A cuboid has eight corners and twelve edges.
  
• Cube:  It is a 3D shape with 6 faces, 12 edges, and 8 vertices. The above drawing of a cube shows shapes that fold into a cube.

Visualization of 3-dimensional Shapes

• A three-dimensional item or shape can appear differently from multiple locations (or sides), allowing it to be drawn from various viewpoints; this is known as visualizing a solid shape.
  
• The front view of a hut, as illustrated above, is a combination of a square with a conical top, while the side and top views are a combination of two rectangular surfaces.
  
• In the image above, one side of a solid has two square surfaces that are vertically connected, the front view has three square surfaces that are arranged in an L shape, and the top view has two square surfaces that are horizontally connected.