IX. MENSURATION. 1. Find the area of (1) The floor of a room 16 feet 8 inches long and 15 feet 9 inches wide. (2) A wall 20 feet 4 inches long and 6 feet 6 inches high. (3) An enclosure 50 yards long and 201 yards wide. (4) The whole surface of a room 22 feet 5 inches long, 18 feet 4 inches broad, and 10 feet 9 inches high. 2. If a board be 9 inches broad, what must be its length if it contain 15 square feet? 3. How many yards of carpet a yard wide will be required for a room 12 yards long by 6 yards I foot 6 inches broad? and how many for another room 221 feet by 19 feet? 4. What will be the cost of carpet yard wide at 3s. 9d. per yard for a room 18 feet 9 inches long and 12 feet 6 inches wide? 5. How many tiles, each 9 inches by 6 inches, will be required to pave a court 24 feet 6 inches long and 15 feet 9 inches wide? 6. Westminster Hall is 237 feet long by 68 wide; Brussels Town Hall 264 by 50: how many more persons could the former accommodate than the latter, allowing of a square yard to each person? 7. How many people can be seated in a room 108 feet long and 55 feet wide if 4 square feet are allowed for each person? And what must be the length of a room 66 feet wide which would hold the same number of people? 8. Find the area of the walls of a room 27 feet long, 23 feet 6 inches wide, and 16 feet high. 9. How many yards of paper 2 feet 3 inches wide are required for the walls of a room 24 feet long, 18 feet 9 inches wide, and 14 feet 2 inches high? 10. If tin foil is sold in sheets 10 inches wide, what length of it will be required to line a box 16 inches wide, 15 inches high, and 20 inches long? 11. What will be the cost of painting the walls of a room 17 feet 3 inches long, 15 feet 5 inches wide, and 13 feet 6 inches high, allowing 54 square feet for windows, &c., not to be painted, at 9d. per square yard? 12. What will it cost to cover a platform 12 feet square and 21 feet high with cloth at 2s. 6d. the square yard? 13. How much paper 20 inches wide will be required for the walls of a room 19 feet 6 inches long, 17 feet 3 inches wide, and 10 feet high? And what will it cost at 21d. per yard? 14. A room is 29 feet long, 18 feet 3 inches wide, and 15 feet 6 inches high. Find (1) The area of the floor. (2) The area of the walls. (3) The cost of a cornice 18 inches decp all round the room at 3s. 6d. the square yard. 15. If the ceiling of the room in Question 13 is painted at 2s. 1 d. per square foot, and a cornice 5 inches deep is run round at Is. 3d. per square foot, what is the cost of these decorations? 16. A room 20 feet 3 inches long by 15 feet 9 inches wide is painted at 3d. per square yard, and costs 27s.: what is the height of the room? 17. The area of the floor of a room 24 feet 3 inches long is 42 square yards I foot 132 inches: what is the breadth? And if the cost of painting the four walls at 45. per square foot be 1837. 12s. 4d., find the height of the room. 18. A rectangular enclosure, 50 yards 2 feet 3 inches long, and 20 yards I foot 6 inches wide, has a path 4 feet 6 inches wide taken out of it all the way round: what is the area of the remaining space? 19. A path 6 feet wide is made across a field at one end and down one side. If the field is 79 yards long and 64 yards wide, what is the area of the path? And what part is it of the whole field? 20. How many cubic feet of air are there in a room which is 90 feet long, 40 feet wide, and 223 feet high? And by how much would the volume be increased by raising the ceiling 9 inches? 21. If the length of a cubit be 22 inches, what is the solid content of a room 120 cubits long, 18 high, and 45 broad? 22. A certain trench being 50 feet long, 4 feet wide, and 21 feet deep, what will be the depth of another trench which, being 45 feet long and 5 feet wide, contains 50 cubic feet less than the other? 23. What length of a plank 6 inches broad and 4 inches thick will be equivalent to a solid foot? 24. What is the depth of a cistern whose base contains 15 square feet, and which holds 2 cubic yards of water? 25. A hollow rectangular vessel, formed of material one inch thick, and whose external dimensions are 13 feet 6 inches, 6 feet 8 inches, and 6 feet II inches respectively, weighs I cwt. I qr. and 10 lbs. Find the weight of a solid mass of the same material and the same external dimensions. X. SIMPLE PROPORTION. 1. If 14 cwt. 12 lbs. of sugar cost 461. Is. 8d., what would be the cost of 18 cwt. 63 lbs. ? 2. If a railway fare for 574 miles be 11s. 6d., what ought to be the fare for 2161 miles? 3. If a quantity of wheat fills 1155 sacks, each holding 8 bus. O pks. I gal., how many sacks will it take to contain it, each holding 6 bus. o pks. o gals. 3 qts.? 4. A watch loses 2 hrs. 13 min. a week: how much does it lose in 36 hours? 5. If a person travelling 12 hours a day perform a journey in 24 days, in what length of time will he perform the same journey if he travel 16 hours a day? 6. A railroad running inland for 56 miles has to reach a level 896 feet above its terminus on the coast: shew that the average inclination of the line is I foot in 330. 7. How much carpet at 7s. 6d. per yard must be given in exchange for 84 reams of paper at 11. 12s. 6d. per ream? 8. How much wine at 27. 10s. per dozen must be given in exchange for 3 puncheons of rum at 60l. 8s. 4d. per puncheon? 9. A person paid 177. 6s. 6d. income tax at 7d. in the pound: what does he pay at 5d.? 10. What will be the gain to a person whose annual income is 1251, if the income tax is reduced from 16 pence to 7 pence in the £? 11. A merchant failing for 10000l. has goods and debts to the amount of 3750l.: how much can he pay in the pound? 12. If 21 lbs. of cotton cost IS. Id., how much may be bought for 2s. 6d. ? 13. If of a yard cost of 1l., what will 11 of a yard cost? 14. If of an estate be worth 10037. 17s. Id., what is the value of of it? 15. If 45 oz. Av. cost 831s., what will 813 lbs. cost? 16. A and B start at a distance of 64 miles from each other; A walks 34 miles in the hour, B 24; if they start at the same time how many miles will each walk before they meet? 17. If 4 men or 6 women can do a piece of work in 20 days, how long will 3 men and 5 women take to do it? 18. A garrison of 2310 men is provisioned for half a year; at the end of six weeks they receive a reinforcement of 500 men: how long will their provisions now last, reckoning 365 days to the year? 19. If a man earns 77. 1os. in 3 weeks, and lays by one-half of it, how much will he save in a year of 52 weeks? 20. From what property of Proportion is the Rule of Three derived? If a bankrupt has assets to the amount of 1020., and debts to the amount of 3225%, what will his creditors receive in the £? XI. COMPOUND PROPORTION. 1. If 27 men earn 357. in 8 days, how much will 18 men earn in II days? 2. If 7 men will earn 10l. 7s. 6d. in 101 days, what sum will 28 men earn in 314 days? 3. If it costs 867. 8s. to maintain 48 men for 16 days, how much will it cost to maintain 32 men for 12 days? |