2D and 3D Shapes

The objects around us come in various shapes and sizes. In general, we can see shapes such as triangles, squares, and circles everywhere around us. Moreover, shapes such as a sheet of paper, have only length and breadth. Thus such shapes are 2D or two-dimensional. While other shapes such as the shape of a house, have length, breadth, and height. Thus such shapes are 3D or three-dimensional.  Let’s learn more about 2D and 3D shapes!

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2D Shapes

In geometry, a shape or a figure that has a length and a breadth is a 2D shape. In other words, a plane object that has only length and breadth is 2 dimensional. Straight or curved lines make up the sides of this shape. Also, these figures can have any number of sides. In general, plane figures made of lines are known as polygons. For example, triangles and squares are polygons.

Because 2D objects have no depth, they cannot be physically held; a 2D shape is absolutely flat. Plane shapes are another term for 2D shapes: a two-dimensional, closed, or flat plane shape. A sheet of paper, for example, has a two-dimensional shape. It has two dimensions: length and breadth, but no depth or height.

Examples of 2D shapes

Rectangle, circle, square, triangle, quadrilateral and pentagon are some examples of 2D shapes.

Types of 2D Shapes

2D shapes are further classified into 2 types – regular or irregular – based on their length and interior angles.

• A 2D shape is considered to be regular if all of its sides have the same length and all of its interior angles are of the same measurement.
• A 2D shape is irregular if all of its sides are unequal in length and all of its angles are unequal in measurement.

Properties of 2D Shapes

Regular and irregular 2D shapes include the circle, triangle, square, rectangle, pentagon, and hexagon. Let us look at a few of them and their properties.

1. Circles –

Circles are entirely round shapes formed by a single curved line. The curved line’s points are at equal distances from its centre.

A semi-circle has two sides, one curved and one straight. The entire arc has a 180° angle.

2. Triangles (3 sides) –

A triangle is a closed polygon with three sides, three vertices, and three angles. The sum of the triangle’s three interior angles is 180°.

An equilateral triangle is a regular triangle with 60° angles each.

Any triangle with one right angle is referred to as a right-angled triangle.

A scalene triangle is an irregular triangle wherein every side and angle is unique.

An isosceles triangle has two equal sides and two equal angles.

3. Quadrilaterals (4 sides) –

A square is a regular quadrilateral with all vertices at 90° angles.

A kite has two sets of equal-length sides, with diagonals intersecting at right angles.

A rectangle is made up of two parallel straight lines, each with a 90° angle.

A rhombus is defined by two parallel lines, equal sides, and opposite equal angles.

A trapezium has one parallel pair of lines.

A parallelogram is made up of two parallel lines and two opposite equal angles.

4. Polygons (4+ sides) –

A 5-sided shape is called a Pentagon. Interior angles add up to 540°.

A 6-sided shape is called a Hexagon. Interior angles add up to 720°.

A 7-sided shape is called a Heptagon or Septagon. Interior angles add up to 900°.

An 8-sided shape is called an Octagon. Interior angles add up to 1080°.

A 9-sided shape is called a Nonagon. Interior angles add up to 1260°.

A 10-sided shape is called a Decagon. Interior angles add up to 1440°.

3D Shapes

A three-dimensional shape is defined in geometry as a solid figure or an item or shape with three dimensions — length, breadth, and height. In our day to day life, we see several objects around us which have different shapes. For example, books, balls, ice-cream cones etc. One thing common in these objects is that they all have some length, breadth and height or depth. Thus they have three dimensions and so are known as 3D shapes. The D in 3D stands for dimensional. 3D shapes occupy space. In a world with three dimensions, you can travel forward, backward, right, left, and even up and down.

Examples of 3D Shapes

Cuboid, cube, cylinder, sphere, pyramid and cone are a few examples of 3D shapes

 

Understand the concept of Polyhedron here in detail.

Types of 3D Shapes

In mathematics and real life, there are many 3D shapes and objects with different bases, surface areas and volumes. Let us look at a few of the most commonly seen 3D shapes.

• Sphere 

  A sphere is round and circular in shape. All the points on the surface of the sphere are equidistant from the centre. It has the following dimensions: radius, diameter, circumference, volume, and surface area. There is only one face, no edges, and no vertices. For example, a ball, lemon, etc.

• Cube and Cuboid 

  The cube and cuboid have the same number of faces, vertices, and edges. The major distinction between a cube and a cuboid is that a cube has all six faces that are squares, whereas a cuboid has all six faces that are rectangles. For example, ice cube, Rubik’s cube, etc.

• Cylinder 

  A cylinder is a three-dimensional shape with two round faces, one at the top and one at the bottom, as well as one curving surface. A cylinder has a radius and a height. It is a 3D object with two identical round or oval ends. For example, candles, batteries, cans, etc.

• Cone 

  A cone has a flat (circle-shaped) base and a pointy tip at the top. The pointy end at the top of the cone is referred to as the ‘Apex.’ A cone has a curved surface as well. For example, ice-cream cone, party hat, Christmas tree, etc.

• Torus 

  A torus, often known as an O ring, is a doughnut-shaped object. It is created by spinning a smaller circle with a smaller radius (r) around a larger circle with a larger radius (R). For example, tire, ring, doughnut, etc.

• Pyramid 

  A pyramid has a polygon base and an apex with straight sharp edges and flat faces. Types of pyramids –

  • Tetrahedron – Pyramid with a triangular base
  • Square Pyramid – Pyramid with a quadrilateral base
  • Pentagonal Pyramid – Pyramid with a pentagon as base
  • Hexagonal Pyramid – Pyramid with a hexagon as base
  • Octagonal Pyramid – Pyramid with an octagon as base

• Prism 

  A prism is a 3D form that consists of two similar shapes that face each other. Prisms are classified into several types, including triangular prisms, square prisms, pentagonal prisms, hexagonal prisms, and so on.

• Polyhedrons 

  A three-dimensional form having flat polygonal faces, straight edges, and sharp corners or vertices is known as a polyhedron. Polyhedrons are further classified into Prisms, Pyramids and Platonic Solids (Eg. Octahedron, Dodecahedron, Icosahedron).

3D Shapes Formulas

Every three-dimensional shape has a surface area and a volume metric. The surface area is the area occupied by the 3D shape at the bottom, top, and all faces, including any curved surfaces. A 3D shape’s volume is defined as the amount of space it takes up.

3D Shape	Formulas
Sphere	Diameter = 2 x r Surface Area = 4πr2 Volume = (4/3)πr3
Cylinder	Total Surface Area = 2πr(h+r) (where r = radius and h = height of the cylinder) Volume = πr2h
Cone	Curved Surface Area = πrl (where l = slant height and l = √(h2 + r2)) TSA = πr(l + r) Volume = (1/3) πr2h
Cube	Lateral Surface Area = 4a2 TSA = 6a2 Volume = l x b x h
Cuboid	LSA = 2h(l + w) TSA = 2(lw + wh + lh) Volume = l x w x h
Prism	Surface Area = [(2 x Base Area) + (Perimeter x Height)] Volume = Base Area x Height
Pyramid	Surface Area = Base Area + (1/2 x Perimeter x Slant Height) Volume = [(1/3) x Base Area x Altitude]

3D Shapes – Faces, Edges, and Vertices

Let us take an example. The object below is a cube.

The corners of the cube are its vertices. The 12 line segments that form the skeleton of the cube are its edges. The 6 flat square surfaces that are the skin of the cube are its faces. Observe that the two-dimensional figures can be identified as the faces of the three-dimensional shapes. For example, a cylinder has two faces which are circles. Also, a pyramid has a triangle on its face.

3D Shapes	Faces	Vertices	Edges
Sphere	1	0	0
Cylinder	3	0	2
Cone	2	1	1
Cube/Cuboid	6	8	12
Rectangular Prism	6	8	12
Triangular Prism	5	6	9
Pentagonal Prism	7	10	15
Hexagonal Prism	8	12	18
Square Pyramid	5	5	8
Triangular Pyramid	4	4	6
Pentagonal Pyramid	6	6	10
Hexagonal Pyramid	7	7	12

You can download Visualising Solid Shapes Cheat Sheet by clicking on the download button below

Nets for building 3-D shape

A net is a two-dimensional representation of a three-dimensional figure that is unfolded along its edges. It represents each face of the figure in two dimensions. In other words, a net is a pattern made when the surface of a three-dimensional figure is laid out. Thus showing each face of the figure. A solid may have different nets.

For example, a box is solid. It’s a 3D object with the shape of a cuboid. Below is a net pattern for a box. Copy an enlarged version of the net and try to make the box by folding and glueing the faces together. You may use suitable units.

Furthermore, different shapes have different nets.

Get Maths Important Questions here

FAQs on 3D Shapes

Question 1: Which of the following is true for a polyhedron?

1. Polyhedrons are 3D figures.
2. They always have a closed surface.
3. A line joining any two points on the surface always lies inside the shape.
4. Both bases are parallel to each other.

Answer : (i) and (ii) are true.

Question 2: What are 2D shapes?

Answer: 2D shapes refer to all those shapes that we can lay on a flat piece of paper or any mathematical plane. The most common example of 2D shapes is the drawing of squares, triangles, and circles that you make in childhood. Besides, 2D shapes exist all around the world.

Question 3: How many 2D shapes are there. List some of them.

Answer: Some of the most common 2D shapes are triangle, square, rectangle, polygon, pentagon, hexagon, heptagon, octagon, nonagon, decagon, etc. However, there are countless shapes that go on from triangle to n-gon where n represents the number of sides.

Question 4: What are the properties of 2D shapes?       

Answer: There are no fixed properties of the 2D shape. As each shape have a different number of sides and for each shape, properties vary. But, every 2D shape is flat and is enclosed.

Question 5: Can 2D shapes be held?

Answer: No, we cannot hold 2D shapes because they appear on a piece of paper or card that the 2D shapes are drawn on. Although you cant’ hold 2D shapes themselves. Besides, these flats are not flat because if you make a pile of them, then they have height and you can hold them.