Right Prism Area
The lateral area L (area of the vertical sides only) of any
right prism is equal to the perimeter of the base times the height
of the prism (L = Ph).
The total area T of any right prism is equal to two times the
area of the base plus the lateral area.
Formula: T = 2B + Ph
Example: Example Figure
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Formula: V = Bh
Example: Example Figure
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Pyramid Volume Theorem
The volume V of any pyramid with height h and a base
with area B is equal to one-third the product of the
height and the area of the base.
Formula: V = (1/3)Bh
Example: Example Figure
A regular pyramid is a pyramid that has a base that is a regular polygon and with lateral faces that are all congruent isosceles triangles.
Regular Pyramid Area Theorem
The area L of any regular pyramid with a base that
has perimeter P and with slant height l is equal to
one-half the product of the perimeter and the slant height.
Formula: L = .5Pl
Example: Example Figure
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Formula: V = (PI)(r^2)h
Example: Example Figure
For any right circular cylinder with radius r and height h, the total area T is two times the area of the base plus the lateral area (2(PI)rh).
Formula: T = 2(PI)rh + 2(PI)r^2
Example: Example Figure
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Formula: V = (1/3)(PI)(r^2)h
Example: Example Figure
Cone Area Theorem
The total area T of a cone with radius r and slant
height l is equal to the area of the base plus PI times the product of the radius and the
slant height.
Formula: T = (PI)rl + (PI)r^2
Example: Example Figure
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Volume Formula: V = (4/3)(PI)r^3
Area Formula: A = 4(PI)r^2
Example: Example Figure
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Take the quiz on area and volume of solids. The quiz is very useful for either review or to see if you've really got the topic down.
