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Let p be the perpendicular, a the apothem of one face, A one-half of a dihedral angle, n' the number of sides of one face, and e one edge.

p = a tan A, a e cot180°. Article 166.
.. p

e cot 180° tan A.

Let k', n, and k be the same as in article 198. Then, pk the volume of the polyhedron. ... v = nk'e3 cot 180° tan A.

Let e =

=

Names.

1, and verify the table subjoined:

226. Table.

· Tetrahedron

Hexahedron

. Octahedron

Dodecahedron

Icosahedron

[blocks in formation]

227. Application of the Table.

Letv and v denote similar regular polyhedrons whose edges are 1 and e, respectively. Then we have 13 : e3. v = v'e3.

v v

228. Examples.

edge

1. What is the volume of a tetrahedron who is 10 ft.? Ans. 117.8513 cu. ft.

2. The volume of a hexahedron is 134217728 cu. in.; what is its surface? Ans. 1572864 sq. in.

LOGARITHMIC TABLES.

(187)

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