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\fdO'^ - Old Forge Coal Mines

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166 GEOMETRY AND TRIGONOMETRY.<br />

(323) Angle mOB=^oi 360°, mO=\<br />

oi<br />

• or 22^<br />

lb Z Ai<br />

^<br />

»2« = - of 2, or 1 inch. (See Fig. 12).<br />

1°<br />

Side mB = O mx tan 22— ,OTmB =<br />

1 X .41421 = .41421.<br />

AB=2i}tB; therefore, AB=. 82842<br />

inch.<br />

Area of A O B =z\ x .82842 X 1 =<br />

.41421 square inch, which, multiplied<br />

by 8, the number of equal triangles,<br />

equals 3.31368 square inches.<br />

Wt. of bar equals 3.31368 X 10 X 12 X .282, or 112 pounds<br />

2 ounces. Ans.<br />

(324) 16 X 16 X 16 X ^ X 3.1416 = 2,144.66 cu. in.<br />

equals the volume of a sphere 16 inches in diameter,<br />

12 X 12 X 12 X TT X 3.1416 = 904.78 cu. in. equals the<br />

volume of a sphere 12 inches in diameter.<br />

The difference of the two volumes equals the volume of<br />

the spherical shell, and this multiplied by the weight per<br />

cubic inch equals the weight of the shell. Hence, we have<br />

(2,144.66 - 904.78) X .261 = 323.61 lb. Ans.<br />

gi 3 y 3g()<br />

(325) The circumference of the circle equals ^^<br />

'<br />

72 ' 0833<br />

'<br />

or 72.0833 inches. The diameter, therefore, equals<br />

^ ,—<br />

or 22.95 inches.<br />

,<br />

,<br />

o. 1410<br />

(326) The number of square inches in a figure 7 inches<br />

square equals 7 X 7 or 49 square inches. 49 — 7 = 42 square<br />

inches difference in the two figures.<br />

1/7 = 2.64 inches is the length of side of square contain-<br />

ing 7 square inches. The length of one side of the other<br />

square equals 7 inches.

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