69. How many pounds avoirdupois would a ball of such iron 30 in. in diameter weigh?

70. If the specific gravity of ice is .921, find the weight and the surface of each of three spheres of ice whose diameters are 1cm, 10cm, and 1m. Which of these spheres would roll first on a plain, in a graduallyincreasing wind?

445. A straight, round stick, cut off square at each end, is called a cylinder.

The area of the convex surface of a cylinder is obtained as follows: Multiply the circumference of one end by the length of the cylinder.

The volume of a cylinder is obtained as follows:

Multiply the area of one end by

the length of the cylinder.

Cylinder.

71. Given a cylinder 10 in. in diameter and 12 in. long; required the area of each end, the convex area, the total area, and the contents in gallons.

72. Find the capacity in gallons of a round cistern 13 ft. in diameter and 9 ft. deep.

73. What must be the diameter of a cylinder 10 in. deep, in order that it may hold 1 gallon?

74. Find the volume of a cylinder 8 in. in diameter and 11 in. high.

75. Find the dimensions of three cylinders that have the diameters equal to the heights, and hold 1 gal., 1 qt., and 1' respectively.

446. A solid with two equal polygonal ends, connected by plane faces at right angles to the ends, is called a prism. The volume of a prism is found as follows:

Multiply the area of one end by the length of the prism.

IAA

Prism.

Pyramid.

Cone.

76. Find the volume of a triangular prism 11 in. long, the sides of the ends being 2, 3, and 4 in. long.

77. Find the capacity in bushels of a bin 6 ft. long, and the end of which is a square measuring 3 ft. 3 in. on a side. 78. Find the number of cubic yards in a square prism 200 ft. on a side, and 40 ft. long.

447. A solid with a polygonal base, and plane faces meeting in a point, is a pyramid. The volume of a pyramid is one-third of that of a prism of the same base and height. 79. How many cubic yards in a square pyramid 210 ft. on a side, and 123 ft. high?

80. Find the capacity of a cup, the mouth of which is a square 4 in. on a side, and the sides of which are four equilateral triangles.

81. The largest of the Egyptian pyramids is 147m high, with a base 231m square. Find its volume in cubic

meters.

448. A body whose base is a circle, and whose convex surface tapers uniformly to a point, is called a cone.

The volume of a cone is one-third the volume of a cylinder of the same base and height.

82. The slant depth of a conically-shaped drinking-cup is 93mm, and the diameter at the top 8cm. What is its capacity?

83. The volume of a cone is 1cbm; its height is equal to the radius of its base. Find the dimensions of the cone.

449. The capacity of a round vessel, that is not hemispherical, cylindrical, or conical, may be estimated as follows:

Add one-fourth of the square of the diameter to one-third of the square of the depth, and multiply the result by elevensevenths of the depth.

84. Find the capacity of a wash-bowl 30cm in diameter and 5cm deep.

85. Find the capacity in liters of a boiler 89cm in diameter and 31cm deep.

86. Find the capacity in quarts of a bowl 10 in. in diameter and 4 in. deep.

87. Find the capacity in pints of a saucer 6 in. across and 11⁄2 in. deep; of a bowl 7 in. across and 3 in. deep; of a bowl 8 in. across and 3 in. deep.

88. How many gallons will a boiler 5 ft. in diameter and 2 ft. deep hold?

89. How many gallons will a boiler 30 in. in diameter and 1 ft. deep hold?

90. Find the capacity in pints of a cylinder 1.9375 in. in diameter, 2.4375 in. high; of a cylinder 3 in. in diameter, 3 in. high; of a cylinder 313 in. in diameter, 51 in. high.

91. Find the capacity in pecks of a cylinder 15.865 in. în

diameter, 12.5 in. high; of a cylinder 9.25 in. in diameter, 4.25 in. deep; of a cylinder 18.5 in. in diameter, 8 in. deep.

92. What must be the diameter of a circle, in order that it may contain 78.54 sq. ft.? to contain 314.16 sq. ft.? 93. What must be the diameter of a circle to contain 1 A. ? to contain 9 A.?

94. What must be the diameter of a circle to contain 1ha ? to contain 25ha?

95. Find the number that exceeds its square root by 20. 96. How much water will a hemispherical bowl hold that is 10 in. in diameter ?

97. What will it cost to gild a hemispherical dome 10 ft. in diameter, at 50 cents a square foot?

98. If the moon is a sphere 2170 miles in diameter, about

how many million bushels would she hold if hollow?

and how many yards of cloth a yard wide would it take to cover her?

99. If the earth is 7920 miles in diameter, and the air is 40 miles deep, how many cubic miles of air are there about the planet?

100. What is the difference between 2 feet square and 2 square feet? between a foot square and a square foot? between half a foot square and 6 in. square?

450. When the top of a cone or pyramid is cut off parallel to the base, the volume of the remaining frustum may be found as follows:

Find the volume of the whole, and also of the part cut off. The difference between the two volumes is the volume of the frustum; or,

Multiply the area of the base of the frustum by that of the top; extract the square root of the product; to the result add the areas of the base and top, and multiply one-third this sum by the height of the frustum.

101. Find the volume of a square frustum of which the base is 3 ft. square, top 2 ft. square, and height 4 ft. 102. Find the capacity in liquid quarts of a tin pan 10 in. in diameter at top, 8 in. in diameter at bottom, and 4

in. deep.

103. How many hektoliters will a circular vat hold 5m in diameter at the top, 4.57m at the bottom, and 1.17m deep?

451. The oval made by the shadow of a circular plate is called an ellipse.

The area of an ellipse is .7854 of the product of its longest and shortest diameters.

104. Find the area of an ellipse 8 in. by 11 in.; of an ellipse 15 in. by 21 in.

105. The ends of a cord 100 ft. long are fastened to stakes placed 80 ft. apart on level ground. A ring, to which a kid is tied, plays freely on the cord. How far from the straight line joining the stakes can the ring be pulled? What are the diameters of the ellipse which the kid can graze? How many square feet in the ellipse?

106. Using the same rope as in the last problem, but putting the stakes 25 ft. apart, how many per cent is the kid's pasturage increased?