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Volume & Surface Area of Simple 3-D Objects
Cubes

 

 

A cube is a special type of cuboid where each of the six faces are squares.

The volume of a cube = side x side x side = side3

 

 

The surface area of a cube = sum of the area of the 6 faces

 

Prisms

 

A prism always has two parallel and congruent faces called bases. The bases are themselves polygons. If the 2 bases of a prism are aligned to be one directly above the other, then it is a ?right prism?, otherwise, it is called an ?oblique prism?.

 

Below is an example of a right, ?triangular prism?:

Below is an example of right, ?rectangular prism?:

 

 

Below is an example of an oblique rectangular prism:

 

The volume V of a prism is the area of the base B times the height h

 

 

The surface area of a prism is the sum of the area of all its faces (base faces and side faces).

 

Cylinders

 

A cylinder is very similar to a prism, in that it also has two parallel and congruent faces called bases. However, a cylinder?s bases are circles, not polygons. If the 2 bases of a cylinder are aligned to be one directly above the other, then it is a ?right cylinder?, otherwise, it is called an ?oblique cylinder?.

 

Below is an example of a right cylinder:

 

 

Below is an example of an oblique cylinder:

 

The volume V of a cylinder is the area of the base B times the height h

 

 

The surface area of a cylinder is the sum of the 2 base circles plus the area of its curved surface. You can think of the curved surface of a cylinder as a rectangle, with width the same as the height of the cylinder, and length the same as the perimeter of the base circle. Therefore, the surface area of a cylinder is:

 

 

Where A is the surface area of the cylinder, r is the radius of the base circle, and h is the height of the cylinder.