58

A solid mineral body that has been divided into blocks by a series of

evenly spaced parallel sections is computed by the "end-area" formula derived

from formula (46),

V = (Si + 2S2 + 2S3 + ... + Sn) , (47)

where L equals the distance between sections. If the sections are unevenly

spaced the formula for the volume of the entire body will be

(S1 + Ss) (Sa + S3) (Sn-1 + Sn)

V = - 2 - LI + - 2 -- ! + ..+ - 2 - **' ( ^

where LL , Ig , LQ , ... 1^ are perpendicular distances between the adjoining

sections with areas S- , 82, S3 ... Sn .

Wedge and Cone (Pyramid) Formulas. - End blocks of lens like mineral

bodies may be converted to a wedge or cone (pyramid) with the larger areas S

in one section, tapering to a line or a point in the adjoining section (fig.

38A) . If the block tapers to a line, volume is computed by wedge formula,

V = | L. (49)

This formula, however, is precise only when the base is rectangular and

the lateral faces are isosceles triangles and trapezoids. A more precise

formula for the wedge is ( 42 )

V = i (2a + a: ) b sin a , (50)

6

where a and b are the lengths of sides of the base a - angle between a and b,

and aT is the larger side of the trapezoid (38A right).

If the block tapers to a point (fig. 38J5) , volume is computed by cone

formula ,

V = f L. (51)

Volume computed by the wedge formula is 50 percent larger than volume computed

by the cone formula.

Frustum Formula. - When S^ and 82 vary in size, but are similar (fig.

38) , frustum of a cone or pyramid formula is used to compute the block

volume,

V = - (S1 + % + /sTsT). (52)

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