224 Commercial Gardening 



multiplied by the slant height. Example: The radius of the base of a 

 cone is 8 in. and the slant height 14 in. Circumference of base = 2x8 

 X 3-1416 = 50-2656; and area = i X 14 x 50-2656 = 351-8592 sq. in. 



The rule for finding the area of the surface of a cone may be used for 

 estimating the approximate extent of the leaf surface of many kinds of 

 trees, shrubs, and bushes, which are often conical in shape. Thus a tree 

 or bush having a spread of 10 ft. across the base of the branches, and a 

 slant height of 10 ft. from base to apex, would have an approximate leaf 



, , 10 x 3-1416 x 10 . _,. AQ ,, 

 surface of - ~ = 157'08 sq. ft. 



Zt 



Most flower pots are cones with the ends cut off in other words, a 

 flower pot is a frustum of a cone. To find the area of the curved surface 

 of a flower pot, multiply the sum of the circumferences of the two ends 

 of the flower pot (frustum) by the slant height of the pot (frustum), and 

 half the product will be the area of the curved surface. 



Example: The radius of the bottom or narrow end of a flower pot is 

 10 in., and the radius of the top or broad end is 15 in.; the slant height 

 is 16 in. Find the area of the curved surface. 



The sum of the circumferences in inches is the product of 31416 into 

 the sum of 20 and 30, i.e. into 50. Thus the sum of the circumferences is 

 50 x 3"1416 in. Multiply this sum by the slant height, 16, and divide 



Ifi v ^0 v 

 by 2, thus: 1D X ou * = 8 x 50 x 3-1416 = 400 X 31416 



IB 



= 1256-64 sq. in. 



Cylinder. Hot-water pipes and water cans being really cylinders, it 

 is useful to know their surface areas as well as contents. To find the area 

 of a curved surface of a circular cylinder (like a piece of piping), the rule 

 is to multiply the circumference of the base by the height of the cylinder. 

 It may be remarked that a cylinder is really a rectangle rolled up till 

 its two long edges meet. Thus, if a piece of hot-water pipe is 4 in. in 

 diameter and 3 ft. (36 in.) long, the area of its curved surface will be 

 4 x 3'1416 x 36 = 452'39 sq. in. It is thus easy to find the heat surface 

 of the piping in any greenhouse by means of this rule. The curved surface 

 of a water can may be found in the same way. 



Where, however, it is necessary to know not only the area of the curved 

 surface, but also that of the two ends, the latter is found by the rule for 

 finding the area of a circle (see above). The whole surface of a cylinder, 

 therefore, equals the area of the two ends plus the length multiplied by 

 the circumference. 



Sphere OP Globe. The surface area is found by multiplying the 

 square of the diameter by 31416. Thus a globular bush 5 ft. through has 

 a superficial area of 5 x 5 X 3*1416 = 78'54 sq. ft. 



Triangles. The ends of greenhouses and the gable ends of houses, 

 sheds, &c., from the eaves up, are examples of triangles. To find the area 

 of a triangle the rule is to multiply the base by half the perpendicular 

 height; or the other way round half the bast by the perpendicular height 



