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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,558

Solid Geometry Formulas

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

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,821

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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,821

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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,821

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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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 15,821

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

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)*

The Beginning Of All Things To End.

The End Of All Things To Come.

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

**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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**pulidilip****Member**- Registered: 2008-03-14
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Thanks Brother

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

**Polygon**

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**irspow****Member**- Registered: 2005-11-24
- Posts: 456

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)

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