GRE Coaching Math: Lesson 6 --> Geometry Level 3: Mensuration

There are special formulas that deal with prisms, but they only deal with right prisms.  Right prisms are prisms that have two special characteristics - all lateral edges are perpendicular to the bases, and lateral faces are rectangular.  The figure below depicts a right prism. 

 

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 

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Right Prism Volume Postulate 

The volume V of any right prism is the product of B, the area of the base, and the height h of the prism. 

Formula: V = Bh 

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A pyramid is a polyhedron with a single base and lateral faces that are all triangular.  All lateral edges of a pyramid meet at a single point, or vertex. 

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 

 

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

 

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Cylinder Volume Theorem 

The volume V of any cylinder with radius r and height h is equal to the product of the area of a base and the height. 

Formula: V = (PI)r²h 
 

Cylinder Area Theorem 

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)r² 

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Cone Volume Theorem 

The volume V of any cone with radius r and height h is equal to one-third the product of the height and the area of the base. 

Formula: V = (1/3)(PI)r²h 

 
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)r² 

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Sphere Volume and Area Theorem 

The volume V for any sphere with radius r is equal to four-thirds times the product of PI and the cube of the radius.  The area A of any sphere with radius r is equal to 4(PI) times the square of the radius.

Volume Formula: V = (4/3)(PI)r³

Area Formula: A = 4(PI)r²

Download the complete Lesson and Post any Querries in the comments or send to the Email ID mentioned in the file. 

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