6. Each side of a hexagonal pyramid is 14 ft. and its slant height is 15 ft. Find the area of its lateral surface. 7. A pyramidal tent whose base is a square 22 ft. on a side has a slant height of 30 ft. Find the cost of the canvas for the tent, at 18 per square yard. 8. Find the number of square yards in the lateral surface of a triangular pyramid, each side of the base being 21 ft. and the slant height being 42 ft. 9. The radius of the base of a right cone is 49 in. and the slant height is 50 in. Find its convex surface vor vi its base veng in ft.? 9. How many gallons does a cylindrical cistern contane, the the diameter of its base is 11 ft. and its height is 6ìnt n.? hei o. The diameter of the base of a cylinder is 10è a Cote haight is 10 in. Find the ratio of 1. dnu the slant height 16 ft.? 12. Find the convex surface of a cylinder the diameter of whose base is 19 ft. and whose height is 50 ft. 13. Find the convex surface of a cylinder, the radius of the base being 41 in., and the height, 60 in. 14. A standpipe has a diameter of 30 ft. and is 150 ft. high. Find the cost of painting it at 25¢ per square yard. 15. Find the surface of a sphere whose radius is 98 in. 16. Find the surface of a sphere if its diameter is 42 in. 17. The diameter of the planet Mercury is 3030 mi.; find the area of the planet. 18. The diameter of the planet Venus is 7700 mi.; find the area of the planet. 19. The diameters of the major planets are, respectively, 86,000, 73,000, 32,000, 33,000 mi. Find the number of million square miles in the area of each of these planets. 20. The surface of a sphere is 10,568 sq. in. Calculate its diameter. VOLUMES OF SOLIDS The volume of a rectangular prism is equal to the area of its base multiplied by its height. The volume of a cylinder is also equal to the product of its base by its height. 1-ཨAཐ 10uI IIuce ཅམཔ its great circles, i.e. 4 πr2. EXERCISE 155 1. Find the lateral surface of a quadrangular prism, t mensions of whose base are 16 ft. by 8 ft., and who The volume of a pyramid and that of a cone are each equal to one third the product of the area of the base and height. The volume of a cylinder having r for radius of base and 2r for height is πr2 × 2r= 2 πr3. = The volume of a sphere having r for radius is of 2 πr3 Tr3, and since r = 1⁄2 d, .. r3 = {} ď3 ; 1. Find the volume of a triangular prism, the sides of the base being 11, 25, 30 in., respectively, and the height of the prism being 40 in. 2. Find the volume of a square pyramid, if the sides of the base are each equal to 10 in., and the height is 21 in. 3. Find the volume of a cone, the radius of its base being 12 in., and its height being 27 in. 4. Find the volume of a cone, if the radius of the base is 25 in., and the height is 24 in. 5. Find the volume of a hexagonal pyramid, each side of its base being 10 in., and its height being 30 in. 6. Find the volume of a sphere whose radius is 20 in. 7. Find the volume of a sphere, the radius being 8 ft. 8. How many gallons does a cylindrical cistern hold, the diameter of its base being 9 ft. 4 in., and its height 8 ft.? 9. How many gallons does a cylindrical cistern contain, if the diameter of its base is 11 ft. and its height is 6 ft. 5 in.? 10. The diameter of the base of a cylinder is 10 in., and its height is 10 in. Find the ratio of the volume of this cylinder to the volume of a sphere 10 in. in diameter. 11. The diameter of the base of a cone is 1 ft. and its height is 1 ft. Find the ratio of the volume of this cone to the volume of a sphere whose diameter is 1 ft. 12. The surface of a cube contains 84 sq. ft. 54 sq. in. Find its volume. 13. The base of a pyramid is a triangle whose sides are 1 ft. 1 in., 3 ft. 1 in., 3 ft. 4 in., and whose volume is 1 cu. ft. 1152 cu. in. Find its height. 14. The surface of a sphere equals 1257 sq. in. Find its volume. ft. 15. The surface of a hemispherical dome is 2513.5 Find its diameter. sq. 16. The volumes of similar solids are to each other as the cubes of their corresponding dimensions. How many times as large as the earth is the sun? The diameter of the sun is nearly 888,000 mi., and the diameter of the earth is nearly 8000 mi. 17. Find how many times as large as the moon is the earth. The moon's diameter is 2200 mi., nearly. 18. How many times as large as the earth is Saturn? The diameter of Saturn is 73,000 mi. 19. How many times as large as the earth is Jupiter? The diameter of Jupiter is 88,000 mi., nearly. MEASURE OF TEMPERATURE A thermometer is an instrument for measuring heat. The principle of the thermometer is that substances expand with heat, according to a natural law. There are two different styles of thermometer in general use, -the Centigrade and the Fahrenheit. The Centigrade thermometer marks the melting point of ice 0°, and the boiling point of water 100°. The interval between these points is divided into 100 parts, or degrees, so that the change in the volume. of the mercury between any two consecutive marks is of the change from 0° to 100°. The Fahrenheit thermometer divides the interval from the melting point of ice to the boiling point of water into 180°. It marks the melting point of ice 32°, and the boiling point of water 212°. Notation. 92° C. means 92 degrees on the Centigrade thermometer. 45° Fahr. means 45 degrees on Fahrenheit's thermometer. +10° means 10 degrees above zero. (1) To change from degrees Fahrenheit to degrees Centigrade, subtract 32° and multiply the remainder by 5. (2) To change from degrees Centigrade to degrees Fahrenheit, multiply the number of degrees Centigrade by and add 32 to the product. Explanation of the rules: (1) Suppose the temperature on a Fahrenheit thermometer is n degrees. Subtract 32° to get the number of degrees from 0. A difference of 180° Fahrenheit a difference of 100° Centigrade. Therefore, a difference of 1° Fahrenheit = a difference of 5° Centigrade. Therefore, a difference of (n-32°) Fahrenheit (n-32°) Centigrade, which symbolizes the first of the above rules. = g (2) A difference of n° C. = a difference of n° Fahrenheit. Hence, n° C. = (§ n° + 32°) Fahr. |