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.

]]>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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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?*

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:

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..]]>

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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Volume, V

Total Surface Area, or Surface Area,

Solid Hemisphere

Volume, V

Curved Surface Area,

Total Surface Area,

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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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