Learn About Three-dimensional points in Detail

What are 3D shapes?

These are solid shapes or objects with three dimensions (length, breadth and height). Also, they have faces, vertices and edges. They occupy volume and have some depth. 3D shapes are made of 2d shapes, for example, squares and cubes. Square is a 2D shape and has one face, 4 edges and no vertices; cube has 6 faces which have the shape of a square and has 12 edges and 8 vertices. 3D shapes have different categories. Some are pyramids and prisms, and some are curved.

What are the different types of 3D shapes?

There are different types of three-dimensional shapes, and all of them have different bases, volumes and surface areas. So, let’s study them briefly.

Cube:

• Has six faces
• Has 12 edges
• Has 8 vertices
• Its surface area is calculated by using formula 6a2 (a= number of sides)
• Its volume is calculated by using the formula a3
• Has equal length and breadth

Cuboid:

• It also has 6 faces
• 8 vertices
• 12 edges
• Its surface area is calculated by using formula 2(lb+bh+lh), [l is for length, b is for breadth, and h is for height]
• Its volume is calculated by using formula l × b × h
• The opposites sides are equal

Sphere: 

• Shaped like a ball and is perfectly symmetrical
• Has radius, diameter, circumference, volume and surface area
• It has no face, no edges and no vertices
• Its diameter is 2r (r=radius)
• Radius = D/2 (D = diameter)
• The volume of a sphere = 4 ⁄ 3 r³
• The surface area of a sphere = 4πr²

Cylinder: 

• Three-dimensional object with two identical ends, which are either circular or oval
• Volume of a cylinder =π r²h
• Surface area of a cylinder = 2rπ(h +r)

Cone: 

• It has a circular or oval base with an apex or vertex
• It is a rotated triangle
• It is based on the apex that how it is aligned to the centre of the base
• Right cone, in which apex is perpendicular to the centre of the base
• Oblique cone, in which the apex lies away from the centre of the base.
• It has a height and radius and has a slant height that joins the apex to the base.
• Volume of a cone =πr³h/3
• Surface area of a cone = πr(l + r) [ l = √r²+ h²]

Pyramid:

• A pyramid is a polyhedron with a polygon base and apex with straight edges and flat faces.
• A pyramid with a triangular base is called a tetrahedron
• A pyramid with a quadrilateral base is called a square pyramid
• A pyramid with a pentagonal base is called a pentagonal pyramid
• A pyramid with a regular hexagonal base is called a hexagonal pyramid.
• Surface area of pyramid= base area + ½ × perimeter × slant height
• The volume of pyramid =1/3 × base area × altitude

Prisms: 

• These are solids with identical polygon ends and flat parallelogram sides.
• Same cross-section along its length
• There are different types of prisms: triangular prisms, pentagonal prisms, hexagonal prisms, etc. 
• Surface area of prism= base area + ½ × perimeter × height
• The volume of prism = base area × height

Polyhedrons: 

• It is a 3D shape with polygonal faces like triangles, squares, hexagons with straight edges and vertices.
• It is also known as platonic solids.
• Tetrahedron, which has four equilateral triangular faces
• Octahedron which has eight equilateral triangular faces
• Dodecahedron, has twelve equilateral triangular faces
• Icosahedron, has twenty equilateral triangular faces

Conclusion: 

Three-dimensional shapes are part of our day-to-day life, like an ice cream cone, a gas cylinder, or a Rubik’s cube. Every shape has its depth, area and volume, and it’s important to know how to find or measure them as it is a daily part of our lives.