Math Is Fun Forum

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Solid Geometry Formulas

Solid Geometry Formulas

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

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,425

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,

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,425

Re: Solid Geometry Formulas

Solid Sphere
Volume, V

Total Surface Area, or Surface Area,

Solid Hemisphere
Volume, V

Curved Surface Area,

Total Surface Area,

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,425

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,

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,425

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..

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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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The End Of All Things To Come.

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?

pulidilip

Member

Registered: 2008-03-14

Posts: 0

Re: Solid Geometry Formulas

Thanks Brother

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Solid Geometry Formulas

Polygon

     

irspow

Member

Registered: 2005-11-24

Posts: 1,055

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)

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Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

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)

Unfortunately, trigonometry tends to turn more people off than π.

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