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In geometry, a three-dimensional shape can be defined as a figure or solid object that has three dimensions – length, width and height. Unlike two-dimensional shapes, three-dimensional shapes have thickness or depth.
Here’s a list of the 3-D or three-dimensional shapes with their name, pictures and attributes.
| Name of 3D shape: | Picture of 3D shape: | Attributes: | Properties | Volumes | Surface Area |
| Cube | Faces – 6
Edges – 12 Vertices – 8 |
It has 6 Faces, each with 4 edges (and is a square) It has 12 Edges It has 8 Vertices (corner points), each is where 3 edges meet |
(edge length)3 | 6 × (edge length)2 | |
| Rectangular Prism or Cuboid | Faces – 6
Edges – 12 Vertices – 8 |
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| Sphere | Curved Face – 1
Edges – 0 Vertices – 0 |
It has no edges or vertices (corners) It has one surface It is perfectly symmetrical All points on the surface are the same distance “r” from the center |
4⁄3 × π × r3 | 4 × π × r2 | |
| Cone | Flat Face – 1
Curved Face – 1 Edges – 1 Vertices – 1 |
It has a flat base It has one curved side |
1⁄3 × π × r2 × h | π × r × (r + s) | |
| Cylinder | Flat Face – 2
Curved Face – 1 Edges – 2 Vertices – 0 |
It has a flat base and a flat top The base is the same as the top It has one curved side |
π × r2 × h | 2 × π × r × (r + h) |
Note: All three-dimensional shapes are made up of two-dimensional shapes.
Volume of Cubes:
This is a unit cube. It occupies space. The space it occupies is called its volume. The volume of the cube is 1 cubic centimeter, because the length of its sides is 1 cm. (1 unit cube) and its volume is 1 cubic centimeter or 1 cm3.
This figure is made up of three units joined together. The volume is 3 cubic cm (3cm3). Each unit cube is 1 cub.cm and there are three such unit cubes. Thus, we find the volume by counting the number of unit cubes.
Definition of a Cube: A cube is a special type of cuboid whose length, breadth and height are equal. Each face of the cube is a square and all angles are right angles. Cube is thus a special case of a cuboid. It is also called a square prism.
Properties of a Cube:
- It has six faces
- All the faces are congruent
- Each face is parallel to the one opposite to it
- Has 12 edges and 8 vertices
Volume of Cube:
The equation to find the volume of a cube is length by width by height. The volume of any shape is the amount of space the object uses.
Example: A box 4 in. wide, 3 in. high, and 12 in. long, uses 144 in.3 of space.
Finding the volume of a perfect cube, the equation of calculating the volume is:
The volume of a perfect cube is equal to y3 or y . y . y .
Solve the volume of a rectangular cube that has the following qualities:
Width:15 cm.
Length:7 cm.
Height:4 cm.
The formula for a cube is l3
Volume of Cuboids
Definition of a Cuboid: A cuboid is a rectangular prism with six rectangular faces and all angles are right angles. It can also be called a square prism if at least two of the lengths are equal.
Properties of a cuboid:
- It has 6 faces
- Each face is congruent and parallel to the one opposite to it.
- It has 12 edges and 8 vertices
Volume of a Cuboid
Volume of a Cuboid is a measurement of the occupied units of a cuboid. The volume of a cuboid is represented by cubic units like cubic centimeter, cubic millimeter and so on. Volume of a cuboid is the number of units used to fill a cuboid.
Volume is the space inside a 3 dimensional shape
A cuboid is a 3 dimensional shape. Therefore to work out the volume, we need to know the 3 measurements. The volume is found using the formula
Volume = Height x Width x Depth ( V = h x w x d)
Examples:
- Find the volume of the cuboid in the figure below:
Solution:
Length of the cuboid = 5 cm
Breadth of the cuboid = 4 cm
Height of the cuboid = 2 cm
Volume = (5 x 4 x 2)cm3
= 40 cm3
- A box is 9 cm long, 5 cm wide and 2 cm high. Find its volume.
Solution:
Length of a box = 9 cm
Breadth of the box = 5 cm
Height of the box = 2 cm
Volume of the box = Length x Breadth x Height
= (9 x 5 x 2)cm3
= 90 cm3
- The length of a rectangular block is 15 cm, its breadth is 10 cm and height is 8 cm. Find the volume of the block.
Solution:
Length of a rectangular block = 15 cm
Breadth of the rectangular block = 10 cm
Height of rectangular block = 8 cm
Volume of rectangular block = Length x Breadth x Height
= (15 x 10 x 8) cm3
= 1,200 cm3
Quiz
- What are 3D shapes?
- Mention three 3d shapes as well as their properties
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