Learning 3 Dimensional Shapes

   Three dimensional shapes contain 3-dimensions which has length, width and depth. Prism contains a constant cross section while pyramids contain slanting sides that meet at a point.

        Some 3D shapes can be not closed out and outspread into a plane surface such as cubes, pyramids. The outspread shape is known as net of the solid.

        The below figure shows cube with 3-dimensional representation.

cube

 

Some of the Shapes and 3-D representation:

 

Prisms:

      A 3-dimensional prisms, it contains a constant cross section. The cross section at both trimmings of the solid are the same shape and wherever we cut parallel to these trimming gives the similar shape too.

shapes

Pyramid:

       A pyramid contains slanting sides that meet at a point.

shapes

Cylinder:

     It is shows the shape of lou role.

shapes

     From the above learning we can understand the 3-D representation of some shapes.

 

Net shape:

 

     The below figure shows net shape of cube:

cube

Getting nets right:

      A net is capable to fold up into 3D shape.

cube

      From above learning we can understand how to use net shape.

 

3 dimensional shapes:3-D with 1-D surface:

 

Helix:

      Helix is curve in 3-dimensional space and following equation defines helix parameterization in Cartesian coordinates. That is,

         x(t)=cos(t)

         y(t)=sin(t)

         z(t)=t.

      As the parameter t improve the value, point (x(t),y(t),z(t)) find right-handed helix of pitch  2pi and radius 1 about z-axis, in right-handed coordinate system.

      From, above learning we can understand 3-dimensional with 1-dimensional surface.

 

3 dimensional shapes:3-D with 2-D surface:

 

Cone:

      The volume V of conic solid is one of the products of the area A of base and height h. It is defined as,

                       V= (1/3)Ah

      The middle of mass of a conic solid of identical density lies one-quarter of way beginning the middle of mass of base to the vertex, on direct line joining the two.

      From, above learning we can understand 3 Dimensional with 2 Dimensional surface.


I am planning to write more post on Cosine Function with example, math help online tutor. Keep checking my blog.

 

Properties of 3-D shapes:

 

Sphere:

     It has no flat faces, no straight edges. It contains only one curved face.

Cone:

     It has one curved face and one flat face. Its flat surface is circle.

Cube:

     It has 6 flat square surfaces and 12 straight edges and 8 corners.

Cylinder:

     It has one curved surface and 2 flat circular surfaces.

Cuboid:

     It has 6 flat surfaces and all the surfaces are rectangle and it has 12 straight edges and 8 corners.

     From, above learning we can understand properties of 3-dimensional shapes.