5. How many cords in a pile of wood 72 ft. long, 12 ft. wide, and 8 ft. high? 128 cu. ft. 1 cord. = 6. What is the cost of a pile of wood 120 ft. long, 8 ft. wide, and 10 ft. high, at $5.25 per cord? 7. What will be the cost of the bark that can be piled in a shed 120 ft. long, 60 ft. wide, and 15 ft. high, at $6 a cord? 8. What will it cost to dig a cellar for a house 40 ft. long, 32 ft. wide, and 4 ft. 6 in. deep, at $1.50 a cubic yard? A Cylinder. A Cylinder unfolded. 145. A Cylinder is a round body with equal parallel circles for its bases, and having a uniform diameter. The Altitude of a cylinder is the perpendicular distance between its bases. The Convex Surface of a cylinder is the curved surface which bounds it. If the convex surface of a cylinder be unfolded, it will form a rectangle whose length is the circumference of the base, and whose altitude is the height of the cylinder. Hence the RULE. To find the convex surface of a cylinder, multiply the circum ference of the base by the altitude. To find the contents of a cylinder: RULE. To find the contents of a cylinder, multiply the area of the base by the altitude. WRITTEN EXERCISES. 1. Find the convex surface of a cylinder whose altitude is 12 ft. and the radius of the, base 5 ft. 2. How many cubic feet in a cistern 8 ft. deep and 6 ft. in diameter ? 3. What is the convex surface of a cylinder whose altitude is 20 ft. and the diameter of the base 20 ft.? 4. Find the convex surface and the contents of a cylinder 5 ft. in diameter and 30 ft. high. 5. How many cubic feet in a log 24 ft. long and 4 ft. in circumference? 6. A bushel measure is a cylinder 181⁄2 in. in diameter and 8 in. deep; find the contents. 7. What will it cost to paint the outside of a stand-pipe 75 ft. high and 10 ft. in diameter at 10 cents a square yard? 8. How many cubic feet of iron in a tube 30 ft. long whose circumference is 37.6992 inches, the thickness of the material being 2 inches? 9. Which is the larger, and how much, a cylinder whose circumference is 12 feet, or a volume whose base is a square 12 ft. in perimeter, both being 10 ft. high? 10. The volume of a cylinder is 2513.28 cu. ft., and the diameter of the base is 20 ft.; what is the altitude, and what is the convex surface? BINS, TANKS, AND CISTERNS. 146. The capacity of bins is estimated by the bushel, and the capacity of tanks and cisterns by the gallon, barrel, or hogshead. The Standard Bushel of the United States is a cylindrical measure 18 inches in diameter and 8 inches deep. RULE. To find the number of bushels in a bin, divide the contents in cubic inches by 2150.42. Since 1728 is to 2150.42 as 4 is to 5, nearly, for practical purposes of the number of cubic feet will equal the number of bushels. 1. 8 ft. by 4 ft. by 5 ft. 2. 6 ft. by 3 ft. by 10 ft. WRITTEN EXERCISES. Estimate, by taking of the number of cubic feet as bushels, the capacity of a bin = Calculate exactly the capacity of a bin— 5. 4 ft. by 5 ft. by 6 ft. 6. 8 ft. by 4 ft. by 3 ft. 3. 12 ft. by 40 ft. by 8 ft. 4. 20 ft. by 16 ft. by 12 ft. 7. 10 ft. by 12 ft. by 15 ft. 8. 6 ft. by 8 ft. by 10 ft. 9. What is the difference between the exact number of bushels in a bin 3 ft. by 4 ft. by 5 ft. and the number found by estimating of the number of cubic feet as bushels? 10. A bin 8 ft. by 10 ft. by 12 ft. is full of wheat; what is the difference between the exact number of bushels in the bin and the number obtained by estimating as above? 11. A bin 16 ft. long, 10 ft. wide, and 8 ft. high is full of wheat; at 60 cents a bushel how much more is it worth, calculated exactly, than by estimating of the number of cubic feet as bushels? 12. How many barrels of flour can be made from the contents of a bin 16 ft. long, 10 ft. wide, and 8 ft. deep, if it is full of wheat, and if a bushel of wheat makes 50 lb. of flour? 13. How many gallons of water will a cistern 8 ft. deep and 6 ft. in diameter hold? 14. How many barrels of water in a well 4 ft. in diameter, if the water is 15 ft. deep? 15. How many hogsheads of water will a stand-pipe hold whose diameter is 10 ft. and altitude 75 ft.? 16. If a cubic foot of water weighs 1000 oz., how many tons will the water in a stand-pipe whose diameter is 10 ft. and altitude 75 ft. weigh if the stand-pipe be full? 17. If a well holds 20 hhd. of water and is 4 ft. in diameter, how deep is it? 18. What is the depth of a cylindrical measure 4 in. in diameter which will hold a dry gallon of 268.8 cu. in.? BOARDS AND TIMBER. 147. Boards one inch or less in thickness are estimated by the square foot. Thus, a board 16 ft. long, 15 in. wide, and 1 in. or less in thickness contains 16 × 1 = 20 sq. ft. When lumber is more than one inch thick the thickness is taken into account, and the lumber is estimated by what is called a Board-foot, which is 1 foot square and 1 inch thick. Thus, a board 16 ft. long, 15 in. wide, and 11⁄2 in. thick contains 16 X 14 = 30 ft. It is readily seen that 1 Cubic foot = 12 Board-feet. RULE. I. To find the contents of a board, multiply the length in feet by the width in inches, and divide by 12. II. To find the contents of timber more than an inch thick, multiply the length in feet by the width and thickness in inches, and divide by 12. WRITTEN EXERCISES. How many board-feet in a board 1. 16 ft. long, 9 in. wide, and 1 in. thick? 3. 15 ft. long, 8 in. wide, and 2 in. thick? 6. 12 ft. long, 3 in. wide, and 4 in. thick? 10. 15 ft. long and 12 in. square? 11. 18 ft. long and 6 in. square? 12. What will 20 scantling 16 ft. long, 3 in. wide, and 4 in. thick cost, at $25 per thousand? 13. What cost 40 boards 16 ft. long, 15 in. wide, and in. thick, at $30 a thousand? 14. What is the cost of 5 girders, each 50 ft. long, 14 in. wide, and 12 in. thick, at $30 per M.? 15. What will it cost to enclose a rectangular lot 120 ft. long and 90 ft. wide with a tight board fence 6 ft. high, if the boards are worth $24 per M.? 16. What will it cost to lay a floor 80 ft. long and 60 ft. wide at $35 a thousand, adding for grooving? |