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#1 2006-03-29 10:01:56

MathsIsFun
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Registered: 2005-01-21
Posts: 7,535

Solid Geometry Formulas

Solid Geometry Formulas


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

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#2 2006-04-02 01:46:37

ganesh
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Registered: 2005-06-28
Posts: 13,825

Re: Solid Geometry Formulas

Cube:-
Let the length of the cube be a.
Volume = a³ and Total Surface Area=6a²

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=√(r²+h²).


Curved Surface Area,

Total Surface Area,


Character is who you are when no one is looking.

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#3 2006-04-03 03:33:45

ganesh
Moderator
Registered: 2005-06-28
Posts: 13,825

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.

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#4 2006-04-03 03:45:56

ganesh
Moderator
Registered: 2005-06-28
Posts: 13,825

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.

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#5 2006-04-07 22:56:47

ganesh
Moderator
Registered: 2005-06-28
Posts: 13,825

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.

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#6 2006-06-18 07:05:47

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

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 (2006-06-18 07:07:18)


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#7 2006-08-05 13:02:54

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

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 = πr² 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?

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#8 2008-03-14 05:50:49

pulidilip
Member
Registered: 2008-03-14
Posts: 0

Re: Solid Geometry Formulas

Thanks Brother

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#9 2008-03-14 07:27:15

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Solid Geometry Formulas

Polygon

     


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#10 2011-07-31 14:12:18

irspow
Member
Registered: 2005-11-24
Posts: 455

Re: Solid Geometry Formulas

or...

A = s²/(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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