How To Find The Area Of The Sector Of A Circle

Rule

Multiply the length of the arc D G E by its radius D C, and half the product is the area.

The length of the arc D G E equal 9½ feet, and the radii C D, C E, equal 7 feet, required the area.

9.5X7 = 66.5 / 2 = 33.25 the area.

How To Find The Circumference Of An Ellipse

Rule

Multiply half the sum of the two diameters by 3.1416, and the product will be the circumference.

Example

Suppose the longer diameter 6 inches and the shorter diameter 4 inches, then 6 added to 4 equal 10, divided by 2 equal 5, multiplied by 3-1416 equal 15.7080 inches circumference.

How To Find The Area Of An Ellipse

Rule

Multiply the longer diameter by the shorter diameter, and by -7854, and the product will be the area.

Example

Required the area of an ellipse whose longer diameter is 0 inches and shorter diameter 4 inches.

6 X 4 X .7854 == 18.8496, the area.

How To Describe A Lip To A Measure

Fig. 14.

Let the circle A B represent the size of the measure ; span the dividers from K to F three-quarters of the diameter; describe the semicircle D K E ; move the dividers to G the width of the lip required, and describe the semicircle K P J, which will be the lip sought.

How To Describe A Heart

Fig. 17.

Draw an indefinite line A B; then span the dividers one-fonrth the width you wish the heart, and describe two semiciroumferences A C and C B; span the dividers from A to B, the width of the heart, and describe the lines A D and B D, which completes the description.

How To Find The Centre Of A Circle From A Part Of The Circumference

Fig. 21.

Span the dividers any distance you wish, and place one foot on the circumference A B, and describe the semicircumferences C D, E F, G H, and I K, and through the points of their intersection P Q and R S, draw two indefinite lines L M and N O; the point of their intersection T, will be the centre desired.

How To Find The Contents Of A Pyramid Or Cone

Rule

Multiply the area of the base by the height, and one-third of the product will be the solid content.

Example

Required the solid content in inches of a Cone or Pyramid, the diameter of the base being 8 inches, and perpendicular height 18 inches? 8 X 8 = 64X .7854 X 18=.9047808 / 3= 3015936 inches / 231 = 1 gall. 1¼ qts.