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#1 2006-03-30 09:01:56

MathsIsFun
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Solid Geometry Formulas

Solid Geometry Formulas


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman
 

#2 2006-04-02 23:46:37

ganesh
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Re: Solid Geometry Formulas

Cube:-
Let the length of the cube be a.
Volume = a and Total Surface Area=6a

Cuboid:-
Let the three sides of a cuboid be l, b, and h.
Volume = lxbxh. Total Surface Area = 2(lb+bh+lh)

Right Circular (Solid) Cylinder
If r is the radius of the base and top, and h is the height of the cylinder,
Volume,


Total Surface Area,

Curved Surface Area,


Cone (Solid)

If r is the radius of the base of the cone, and h its height,
its slant height is given by the formula,
l=√(r+h).

Curved Surface Area,

Total Surface Area,


Character is who you are when no one is looking.
 

#3 2006-04-04 01:33:45

ganesh
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Re: Solid Geometry Formulas

Solid Sphere
Volume, V


Total Surface Area, or Surface Area,


Solid Hemisphere
Volume, V

Curved Surface Area,

Total Surface Area,


Character is who you are when no one is looking.
 

#4 2006-04-04 01:45:56

ganesh
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Re: Solid Geometry Formulas

Hollow cylinder.
A hollow cylinder is a solid bounded by two co-axial cylinders of the same height. Let the height be h and external and internal radii be R and r.
Volume of the material used in making the hollow cylinder, V


Curved Surface Area,

Total surface Area,


Character is who you are when no one is looking.
 

#5 2006-04-08 20:56:47

ganesh
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Re: Solid Geometry Formulas

Frustum of a Cone:-

Slant Surface area of the frustum:



where l is the slant height of the frustum.

Volume of the frustum,

where h is the height of the frustum.

Frustum of a pyramid:-

Volume,

where B1 and B2 are areas of the top and the bottom and h is its height..


Character is who you are when no one is looking.
 

#6 2006-06-19 05:05:47

luca-deltodesco
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Re: Solid Geometry Formulas

Torus:
A torus is a 'tube' shape, examples being a doughnut, and an inner tire, let r be the radius of the tube, and R be the distance from the centre of the torus, to the center of the tube

Surface area of the torus:



Volume of the torus:

Last edited by luca-deltodesco (2006-06-19 05:07:18)


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#7 2006-08-06 11:02:54

Zhylliolom
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Re: Solid Geometry Formulas

Parallelepiped

The volume of a parallelepiped of cross-sectional area A and height h is



or, equivalently,



where a, b, and c are the side lengths and θ is the angle between the slanted side and the horizontal.

Slanted Cylinder

The volume of a slanted cylinder with radius r, height h and slant height l is given by



or, equivalently,



where θ is the angle between the slanted side and the horizontal.

The lateral surface area of the slanted cylinder is given by



Non-circular Cylinder

The volume of a non-circular cylinder of cross-sectional area A, height h and slant height l is given by



or, equivalently,



where θ is the angle between the slanted side and the horizontal.

The lateral surface area of the non-circular cylinder is given by



where p is the perimeter of the non-circular cylinder. Note that the equations for circular cylinders may be derived from the equations for non-circular cylinders, by having A = πr and p = 2πr.

Pyramid

The volume of a pyramid of base area A and height h is given by



Spherical Cap

The volume of a spherical cap of radius r and height h is given by



The surface area of the spherical cap is given by



Ellipsoid

The volume of an ellipsoid of semiaxes a, b, and c is given by



Paraboloid of Revolution

The volume of a paraboloid of revolution with "radius" b and height a is given by



Note: Would it be useful if someone were to create labeled images of these shapes to aid in the visualization of them? I could make a few drawings.

Also, should formulas of solid analytic geometry go here as well?

 

#8 2008-03-15 04:50:49

pulidilip
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Re: Solid Geometry Formulas

Thanks Brother

 

#9 2008-03-15 06:27:15

JaneFairfax
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Re: Solid Geometry Formulas

Polygon



     


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#10 2011-08-01 12:12:18

irspow
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Re: Solid Geometry Formulas

or...

A = s/(4tan[180/n]) where s is length of side and n is number of sides (for those who don't want to use pi to calculate the area of a polygon) big_smile

 

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