THREE DIMENSIONAL SHAPES

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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
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:

1. It has six faces
2. All the faces are congruent
3. Each face is parallel to the one opposite to it
4. 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:

1. It has 6 faces
2. Each face is congruent and parallel to the one opposite to it.
3. 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:

1. 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

2. 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

3. 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

1. What are 3D shapes?
2. Mention three 3d shapes as well as their properties

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