3D shapes are solid figures that have three dimensions — length, width, and height. Unlike flat 2D shapes, they have depth and occupy space. Because they take up space, they have volume.
Parts of 3D Shapes
Faces: The flat or curved surfaces of a three-dimensional shape.
Edges: The line segments where two faces meet.
Vertices: The corner points where two or more edges meet.
Basic Properties of 3D Shapes
Three-dimensional (3D) shapes have special properties that make them different from 2D shapes.
- Surface Area: The total area covered by all the outer surfaces of a 3D shape.
- Volume: The space occupied by a 3D shape. It is measured in cubic units.
- Dimensions: Every 3D shape is defined by three dimensions: length, width, and height, which determine its overall size and form.
3D Shapes Around Us
3D Shapes Names
Cube
A Cube is a solid shape or three-dimensional shape that has 6 square faces, 12 edges, and 8 Vertices.
Cuboid
A cuboid, also known as a rectangular prism, where the faces are rectangular. All the angle measures 90 degrees.
Cone
A Cone is a three-dimensional object or a solid that has a circular base that tapers easily to a single point and has a single vertex.
Cylinder
The Cylinder is a three-dimensional shape that has two circular bases connected by a curved surface.
Sphere
The Sphere is a three-dimensional shape where every point on its surface is equidistant from its center. It has no edges, vertices, or flat shapes.
Hemisphere
A Hemisphere is a 3D Shape that represents half of a sphere.
Square Pyramid
A square pyramid is three dimensional geometric shape with a square base and triangular faces that meet at a single point called the apex.
Hexagonal Pyramid
A hexagonal pyramid is a three-dimensional geometric shape with a hexagonal base and has 6 triangular faces.
Triangular Prism
A Triangular Prism is a three-dimensional geometric shape with two identical triangular bases connected by three rectangular faces.
Hexagonal Prism
A hexagonal prism is a three-dimensional geometric shape with two hexagonal bases connected by six rectangular faces.
Other 3D Shapes
A polyhedron is a 3D solid made up of flat polygonal faces, with edges meeting at vertices. Each face is a polygon, and the edges connect the faces at their vertices.
Name | Faces | Vertices | Edges |
|---|---|---|---|
Tetrahedron | 4 faces | 4 vertices | 6 edges |
Octahedron | 8 faces | 6 vertices | 12 edges |
Dodecahedron | 12 faces | 20 vertices | 30 edges |
Icosahedron | 20 faces | 12 vertices | 30 edges |
3D Shapes formulas
Here is the list of formulas for 3D shapes, including surface area and volume:
3D shape | Surface Area | Volume |
|---|---|---|
Cube | 6a2 | a3 |
Cuboid | 2(lb + bh + hl) | 2h(l + b) |
Cone | πr(r + l) ( here l is slant height ) | 1/3πr3 |
Cylinder | 2πr(r + h) | πr2h |
Sphere | 4Ï€r2 | 4/3Ï€r3 |
Hemisphere | 3Ï€r2 | 2/3Ï€r3 |
Square Pyramid | s2 + 2sl ( here s is the base area ) | 1/3s2h |
Hexagonal Prism | 6sh + 3√3s2 | [(3√3)/2]s2h |
Triangular Prism | (b x h) + (s1 + s2 + s3) | 1/2(bhl) |
Hexagonal Pyramid | 3ab + 3bs | abh |