WRITTEN EXERCISES. 4. What is the area of a floor which is 52 feet 9 inches long and 26 feet wide ? 52.75 Solution. — 52 ft. 9 in. = 52.75 26 feet. The product of the length by 31650 the width gives as the number of 10550 square feet of surface 1371.50 sq. ft., . 1371.50 sq. ft. or 1371 sq. ft. 72 sq. in., which is the Or, area required. 1371 sq. ft. 72 sq. in. 5. The area of a floor is 1371 square feet 72 square inches, and its width is 26 feet. What is its length ? 52.75 ft. = 52 ft. 9 in. 26) 1371.50 Solution. — 1371 sq. ft. 72 sq. 130 in.= 1371.50 sq.ft. As the area 1371.50 sq. ft. is the product of 52 the length and width, the width 195 · must equal the quotient of the 182 area 1371.50 divided by the length 26, which is 52.75 ft. = 130 52 ft. 9 in. 130 6. The base of a triangle is 46 ft. 3 in., and the altitude 35 ft. 6 in. What is its area ? 7. The circumference of a circle is 314.16 feet, and its radius 50 feet. What is its area ? 8. The diameter of a circle is 400 feet. What is its circumference ? 9. The circumference of a circle is 1256.64 feet. What is its diameter ? 10. How many yards of carpeting 1 yard wide will be required to carpet a room 18 ft. long and 15 ft. 6 in. wide ? 11. A room that is 18 ft. 9 in. square requires 50 yards of carpeting. What is the width of the carpeting? 12. How many acres in a field 45 rods long and 48 rods wide ? 13. The diameter of a circle is 15 meters. What is its circumference in feet ? 14. What is the area of the gable end of a house 32 ft. wide, the ridge being 14 ft. 6 in. higher than the base of the gable ? 15. How many hektares in a rectangular meadow 564.50 meters long and 260 meters wide ? 16. What will it cost at 60 cents a square yard to concrete a walk 288 ft. long and 12 ft. 6 in. wide ? 17. A horse is fastened to a stake by a chain 60 feet long. How many square rods of surface can the chain sweep over ? 18. How many square feet of sheet zinc will be required to line a cistern 6 ft. deep, having a square bottom, of which each side is 2 ft. 6 in. ? 19. The capitol at Washington is 751 feet long and 348 feet wide. How many acres does it cover ? 20. On laying the pavement of a court with stones 2 ft. 6 in. long by 9 in. wide, it is found that it requires 75 stones to form one strip extending the whole length of the court, and that 84 strips will exactly cover it. What is the area in square yards, and what is the cost of the pavement at 20 cents a square foot ? VOLUMES. 21. How many cubic feet in a beam 10 feet long, 1 foot wide, and 1 foot deep? In a beam 10 feet long, 1 foot wide, and 2 feet deep ? 22. How many cubic feet in a block of marble 8 feet long, 2 feet wide, and 1 foot thick? In a block 8 feet long, 2 feet wide, and 2 feet thick ? 223. A Rectangular Volume is a body bounded by six rectangles. The Dimensions of a rectangular volume are its length, breadth, and thickness. A Rectangular Voluine. 224. The Contents of a rectangular volume are the space contained within its bounding surfaces. The dimensions of a rectangular volume determine its contents. Thus, A rectangular volume 3 inches long, 3 inches wide, and 2 inches thick, contains in one layer 3 rows of 3 cubic inches, or 9 cubic inches, and 2 such layers, or 2 times 3 times 3 cubic inches, contain 18 cubic inches. That is, The contents of a rectangular volume are equal to the product of its length, breadth, and thickness, taken in the same denomination. Also, One of the dimensions of a rectangular solid equals its contents divided by the product of the other two dimensions. 225. A Cylinder is a round body of uni- c form diameter, whose bases are equal and parallel circles. The altitude of a' cylinder is the straight line joining the centers of the two bases; as the line A B. A Cylinder. 226. The Contents of a cylinder are equal to the product of the area of the base by the altitude. The Curved Surface of a cylinder is equal to the product of its circumference and altitude. WRITTEN EXERCISES. 23. How many cubic feet in a rectangular block 8 feet long, 4 feet 6 inches wide, and 2 feet 3 inches thick ? Solution. — 4 ft. 6 in. = f ft. ; 2 ft. 3 in. = ft. The product of the three dimensions, 8 X X = 81 cu. ft. 24. The contents of a rectangular block 8 feet long and 4} feet wide are 81 cubic feet. What is its thickness ? 8 x 41 = 36 Solution. — The contents of the block are the product of its three dimensions. 81 ; 36 = 21 The product of the length and width is 36. The given product of the three 21 ft. = 2 ft. 3 in. dimensions divided by 36 gives for the thickness 27 ft., or 2 ft. 3 in. 25. What are the contents of a trunk 4 feet long, 21 feet wide, and 18 inches deep? 26. How many cubic feet of space in a room whose dimensions are each 10 feet 6 inches ? 27. A rectangular cistern, whose length is 133 feet and breadth 6 feet, contains 2941 cubic feet of water. What is the depth of the water ? 28. A box is 2 meters long, 15 decimeters wide, and 1 meter deep. What is its capacity ? 29. How many cubic yards of earth must be removed in excavating a cellar 60 feet long, 42 feet wide, and 8 feet 6 inches deep? 30. A block is 3 meters long, 2 meters wide, and 1.45 meters thick. What are its contents ? 31. A circular well is 32 feet deep and 3 feet in diameter. How many cubic yards does it contain ? 32. A roller is 4 feet 6 inches long, and 6 feet 4 inches in circumference. How much surface will it pass over in revolving 36 times ? 227. A Range of wood 8 feet long, 4 feet wide, and 4 feet high, makes a cord of wood (Art. 171). A Cord Foot is 1 foot in length of this range, or 16 cubic feet. WRITTEN EXERCISES. 33. How many cords of wood in a range 32 feet long, 8 feet high, and 4 feet wide ? 34. How many cords of 4-foot wood in a range 64 feet long and 4 feet high ? 35. A range of 4-foot wood is 28 feet long and 64 feet high. How many cords does it contain ? 36. A range of 4-foot wood is 56 feet long. How high must it be piled to contain 10 cords? 37. Wood is loaded upon a cart in 2 piles, 3 feet 6 inches wide and. 4 feet 6 inches high. Allowing the wood to have been cut 4 feet long, how much wood is there on the cart? 38. A shed contains a pile of wood 30 feet long, 16 feet wide, and 12 feet high. What is the value of the wood at $5.25 a cord ? |