Then find the volume of the part cut away and subtract from the whole volume to get the volume of the frustum.

162. Measuring Surfaces and Volumes. Many of the cases which one finds in practical work do not fit these regu

lar forms precisely. It is necessary, then, to divide the whole into a number of parts which will come into one of these classes. The accuracy of the result will depend largely upon

. the judgment used in making these divisions and skill in carrying out the operation.

Example. Fig. 81 shows a deck roof and gives the dimensions. Figure the total area of the roof.

Slant height of roof

82=64
82=64

128=11.31' Area of 8 small triangles A, A, A, etc.: 11.31X8

= 45. 24 sq.ft. in one triangle. 2

ft.

45.24 X8=361.92 sq.ft. in 8 triangles. Area of 2 rectangles B, B:

11.31X18X2=407.16 sq.ft. Area of 2 rectangles C, C:

11.31 X4X2= 90.48 sq.
Area of rectangle D:

18X4=72 sq.ft.
Adding:

361.92
407.16
90.48

Explanation. Divide the roof surface up into triangles and rectangles. Figure the area of each of these separately and then add them all together to get the total area.

SUMMARY OF CHAPTER XIV

=

84. The area of a triangle is equal to one-half the product of the base by the altitude. S=ba. (Sec. 152.)

85. The lateral area of a cylinder equals two times a times the radius of the base times the height. S=2trh. (Sec. 154.)

86. To get the total area of a cylinder add to the lateral area the area of both bases. S=2nrh+2rr2. (Sec. 154.)

87. The lateral area of a cone equals a times the radius of the base times the slant height. S=tra.

S= (Sec. 155.) 88. To get the total area of a cone add to the lateral area the area of the base. S=uratora. (Sec. 155.)

89. The volume of a cylinder is equal to a times the square of the radius of the base times the height. V=arah. (Sec. 157.)

90. The volume of a prism is equal to the product of the area of the base by the height. (Sec. 158.)

91. The volume of a pyramid is equal to one-third the product of the area of the base by the height. V = žabh. (Sec. 159.)

92. The volume of a cone is equal to one-third the area of the base by the height. V = žtrah. (Sec. 160.)

V