Part 35

Circumference of a circle = diameter × 3·1416.

Circumference of circle circumscribing a square = side × 4·443.

Circumference of circle = side of equal square × 3·545.

Length of arc of circle = radius × degrees in arc × 0·01745.

Area of a circle = square of diameter × 0·7854.

Area of sector of a circle = length of arc × ½ radius.

Area of segment of a circle = area of sector − area of triangle.

Side of square of area equal to a circle = diameter × 0·8862.

Diameter of circle equal in area to square = side of square × 1·1284.

Side of square inscribed in circle = diameter of circle × 0·707.

Diameter of circle circumscribing a square = side of square × 1·414.

Area of square = area of inscribed circle × 1·2732.

Area of circle circumscribing square = square of side × 1·5708.

Area of square = area of circumscribing circle × 0·6366.

Area of a parabola = base x ⅔ height.

Area of an ellipse = major axis × minor axis × 0·7854.

Surface of prism or cylinder = (area of two ends) + (length × perimeter).

Volume of prism or cylinder = area of base × height.

Surface of pyramid or cone = ½(slant height × perimeter of base) + area of base.

Volume of pyramid or cone = (⅓)(area of base × perpendicular height).

Surface of sphere = square of diameter × 3·1416.

Volume of sphere = cube of diameter × 0·5236.

Volume of hexagonal prism = square of side × 2·598 × height.

Volume of paraboloid = ½ volume of circumscribing cylinder.

Volume of ring (circular section) = mean diameter of ring × 2·47 × square of diameter of section.

SPECIFIC GRAVITY AND WEIGHT OF MATERIALS.

METALS. ─────────────────────┬───────────────┬───────────────┬─────────────── METAL. │ Specific │ Weight of 1 │ Weight of 1 │ Gravity. │Cub. Ft. (Lb.).│Cub. In. (Lb.). ─────────────────────┼───────────────┼───────────────┼─────────────── Aluminium, Cast │ 2·56│ 160│ 0·0927 Aluminium, Bronze │ 7·68│ 475│ 0·275 Antimony │ 6·71│ 418│ 0·242 Bismuth │ 9·90│ 617│ 0·357 Brass, Cast │ 8·10│ 505│ 0·293 „ Wire │ 8·548│ 533│ 0·309 Copper, Sheet │ 8·805│ 549│ 0·318 „ Wire │ 8·880│ 554│ 0·321 Gold │ 19·245│ 1200│ 0·695 Gun metal │ 8·56│ 534│ 0·310 Iron, Wrought (mean) │ 7·698│ 480│ 0·278 „ Cast (mean) │ 7·217│ 450│ 0·261 Lead, Milled Sheet │ 11·418│ 712│ 0·412 Manganese │ 8·012│ 499│ 0·289 Mercury │ 13·596│ 849│ 0·491 Nickel, Cast │ 8·28│ 516│ 0·300 Phosphor Bronze, Cast│ 8·60│ 536·8│ 0·310 Platinum │ 21·522│ 1342│ 0·778 Silver │ 10·505│ 655│ 0·380 Steel (mean) │ 7·852│ 489·6│ 0·283 Tin │ 7·409│ 462│ 0·268 Zinc, Sheet │ 7·20│ 449│ 0·260 „ Cast │ 6·86│ 428│ 0·248 ─────────────────────┴───────────────┴───────────────┴───────────────

MISCELLANEOUS SUBSTANCES. ────────────┬──────────┬────────── SUBSTANCE. │ Specific │Weight of │ Gravity. │1 Cub. In. │ │ (Lb.). ────────────┼──────────┼────────── Asbestos │ 2·1–2·80 │·076-·101 Brick │ 1·90 │ ·069 Cement │2·72–3·05 │·0984-·109 Clay │ 2·0 │ ·072 Coal │ 1·37 │ ·0495 Coke │ 0·5 │ ·0181 Concrete │ 2·0 │ ·072 Fire-brick │ 2·30 │ ·083 Granite │ 2·5–2·75 │·051-·100 Graphite │ 1·8–2·35 │·065-·085 Sand-stone │ 2·3 │ ·083 Slate │ 2·8 │ ·102 Wood— │ │ Beech │ 0·75 │ ·0271 Cork │ 0·24 │ ·0087 Elm │ 0·58 │ ·021 Fir │ 0·56 │ ·0203 Oak │ ·62-·85 │·025-·031 Pine │ 0·47 │ ·017 Teak │ 0·80 │ ·029 ────────────┴──────────┴──────────