Length of circumference = diameter multiplied by 3 1/7 or more accurately diameter x 3.1416.

Area Of Triangle

Multiply the base by half the perpendicular height.

Area Of Circle

Multiply radius by radius then by 3 1/7. Rules for the ellipse are given in Chapter XXI (Elliptical Work. Construction Of Ellipse)., and for the cylinder, cone, and sphere in Chapters XII., XXVII., and XXVIII.

Volume Of Frustum Of Cone Or Pyramid

Although this has been dealt with in Chapter XII (Conical Articles Of Short Taper). there is still another important method that can be applied in obtaining the volume of a bucket-shaped or other similar vessel, whether circular or not: -

Let a1 = area of small end. ,, a2 = ,, ,, large „ „ a = „ ,, mid-section.

Then volume = height x a 1+ 4a + a2 / 6

Put in the form of a rule it becomes: " Add the areas of the ends to four times the area of the mid-section, multiply by the height, and divide by six."

Useful Data

1 inch = 2.54 centimetres.

1 gallon = 277.274 (277¼ nearly) cubic inches.

1 cubic foot = 6¼ gallons.

1 cubic foot of fresh water weighs 62.3 lb.

(In ordinary calculations 62½ is used.) 1 cubic foot of sea water weighs 64 lb. 1 gallon of fresh water weighs 10 lb. 1 gallon of sea water weighs 10¼ lb.