« ΠροηγούμενηΣυνέχεια »
389. GOVERNMENT LANDS.
Before being brought into market, the public lands of the United States are usually divided by parallels and meridians into townships, each being as nearly as possible six miles square. Each township is divided in the same way into 36 sections, and each section into 4 quarter-sections. The township and sections are numbered and referred to special meridians and base lines, so as to be easily designated and
pointed out on government maps.
6 5 4 3
18 17 16 15
19 20 21
30 29 28 27
8 9 10 11
a. How many square miles in a township? in a section? b. How many acres in a section? in a quarter-section ?
118. What must I pay for the N. W. quarter of section No. 9 of township 5 North, 20 West, meridian Michigan, at $2.50 an acre?
390. RECTANGULAR SOLIDS.
119. How many cubic inches are there in a beam 4 ft. 5 in. long, 8 in. wide, and 4 in. thick?
120. What is the weight of a block of Quincy granite 15 ft. long, 14 ft. wide, and 6 in. high, if 1 cubic foot weighs 165 pounds?
121. How high must a block of freestone be to contain 84 cubic feet, if its length is 4 ft. and its width 3 ft. ?
122. If a bin contains 113 cubic yards, and its height is 2 ft., what is the area of its base?
123. There being 112 cubic feet in a shaft of marble which is 27 in. square at each end, what is its length?
391. Wood Measure.
124. If a pile of wood is 3 ft. 8 in. high and 4 ft. wide, how long must it be to contain 1 cord?
125. At $6 a cord, what is the cost of a pile of wood 33 ft. long, 8 ft. 10 in. high, and 4 ft. wide?
126. If wood is cut in lengths of 3 ft. and piled to a height of 4 ft., how long must the pile be to contain 1 cord?
127. On measuring what I bought for a cord of wood, I found it 8 feet long, 4 feet wide, and only 3 feet 8 inches high. At $5 a cord, how much money should be deducted from the original price?
392. LUMBER AND BOARDS.
Sawed timber and boards, when 1 inch or less in thickness, are generally reckoned by the square foot of surface measure. When more than 1 inch in thickness, they are reckoned in proportion to their thickness. Thus,
2000 sq. ft., 1 inch or less in thickness,
2000 sq. ft., 2 inches thick,
and so on.
2000 ft., board measure, 3000 ft., board measure, =4000 ft., board measure,
128. How many feet of boards of an inch thick will be required to make a fence 2 rods long and 3 feet high?
129. How many feet, board measure, are there in a piece of square timber 10 in. wide, 6 in. thick, and 9 ft. long?
130. How many feet, board measure, are there in 200 pieces of scantling, each 18 ft. long, 4 in. wide, and 2 in. thick?
131. How many feet in 8 boards, each 15 ft. long, 8 in. wide, and 1 in. thick?
132. How many feet, board measure, in a plank 24 ft. long, 3 in. thick, 11 in. wide at one end, and 16 in. wide at the other?
NOTE. First find the average width, which equals one half the sum of the widths at the ends.
133. At $22 a thousand, what is the cost of 20 boards, each 18 ft. long, 1 in. thick, 20 in. wide at one end, and 17 in. wide at the other?
134. Arthur bought wood for Sorrento carving, each piece being 2 feet long and of an inch thick, as follows: white holly, 12 inches wide at 8/ a foot, board measure; black walnut, 18 inches wide at 6; ebony, 9 inches wide at 25; red cedar, 14 inches wide at 10%. What was the cost of the
393. CAPACITY OF CISTERNS, BINS, ETC.
135. I have a cask that contains 2 cu. ft.; how many quarts of berries will it hold? (See Art. 329.)
136. How many gallons of water will a cistern hold that is 3 ft. long, 3 ft. wide, and 21⁄2 ft. deep?
137. If a jar weighs 10 pounds when empty and 74 pounds when full of water, what is its capacity in cubic feet? How many gallons will it hold? (See page 141, Note IV.)
138. How many bushels of wheat can be put into a bin 8 ft. long, 3 ft. 2 in. wide, and 2 ft. 3 in. deep?
In measuring bulky fruits and vegetables, as apples and potatoes, the measures are heaped. Heaped measures fill about more space than the
139. If 24 bushels of wheat can be put into a certain bin, how many bushels of apples might be put into the same bin?
140. How many bushels of beets can be put into a barrel that holds 47 gallons?
141. What is the difference in inches between ‡ of a bushel and 1 cubic foot?
NOTE. The difference being so slight, for rough estimates of the contents of bins, etc., it is sufficiently accurate to call every cubic foot of a bushel, even measure, or of a bushel, heaped measure.
142. A box whose capacity is 50 cubic feet, will contain how many bushels of rye? how many bushels of pears?
394. General Review, No. 3.
143. Change 5 m. 42 rd. 8 ft. to feet.
144. Change 4865 gr. to Troy pounds, ounces, etc. 145. Change cu. yd. to feet and inches.
146. What cost 12 bu. 2 pk. of plums at 6 a pint?
147. What cost 2 qt. 13 pt. of oil at $1.12 a gallon?
148. Change 41′ 42′′ to the decimal of a degree.
149. Change 3 yd. to the decimal of a rod.
150. What part of an A. is 116 sq. r. 884 sq.ft.+ 17 sq.r. 2 sq.ft.?
151. Add 0.44 c. y. to 25 d. 5 h. 4 m.
152. Divide 12 A. less 7 A. 16 r. by 9.
153. Change 2 lb. av. to integers of Troy weight.
154. How many square feet in a garden 4 rd. long and 1 rd. 15 ft. wide?
155. How many cu. ft. of space in a cellar measuring on the inside of the wall 5 yd. 1 ft. in length, 4 yards in width, and 10 feet in depth?
156. What must be the depth of a cistern to contain 420 gallons of water, the base being a square covering 124 sq. ft.?
157. When a cistern 4 feet high is full of water, what weight is supported by every square inch of the base? (See page 141, Note IV.)
158. How many bricks 4 in. by 8 in. will be required to pave a court 20 ft. long and 10 ft. wide? Find the cost at $9 per M. 159. Divide 0.006 by 0.06, multiply the quotient by 0.05, and divide that product by 0.005.
160. Change 0.0625 to a common fraction in smallest terms?
161. How many yards of carpeting of a yard wide must be bought to cover a floor 13 feet square, no allowance being made for matching and no breadth to be divided?
162. What is the difference of time in two places whose longitudes differ 7° 8' 4"?
163. When the difference of time between two places is 3 h. 4m. 6 s., what is the difference of longitude?
164. How many days from Jan. 5, 1876, to March 3, 1877?
395. Miscellaneous Examples.
165. If eggs are worth 30 cents a dozen, and 10 weigh a pound, what are eggs worth by the pound?
166. If I burn 30 lbs. of coal a day, and buy my coal by the long ton, at $7 a ton, what is the cost of my coal for December?
167. How many furrows, each 20 inches wide, will be made in ploughing lengthwise a lot of land which is 6 rd. 1 ft. wide? 168. A quantity of silver weighed 4 lb. 10 oz. 3 pwt. before refining, and 3 lb. 11 oz. 2 pwt. 9 gr. afterwards; what weight was lost in the process?
169. How many square feet on the top and sides of a box that is 3 ft. long, 2 ft. wide, and 2 ft. 6 in. high?
170. What will be the cost of fencing a lot of land 20 rods by 26 rods at 25 cents a foot?
171. Change of a great gross to units of lower denomina
172. Divide an angle of 20° 4′ 5′′ by 9.
173. Dr. Smith's wagon-wheel, which is 3 ft. 4 in. in circumference, turns round 200 times in going from his house to the post-office; how far does he live from the post-office?
174. If a bird can fly 1° in 1 h. 8 m. 15 s., in what time can it fly around the world at the same rate?
175. What is the cost of 137 gal. 2 qt. of vinegar at 50 cts. per gal.?
176. How many bushels of grain will a bin contain which is 10 ft. long, 8 ft. wide, and 5 ft. deep?
177. What is the cost of oil-cloth to cover a floor 12 feet by 16 feet, at 75 cents per square yard?
178. A farmer divided one half of his estate of 350 A. 140 rd. equally between his two daughters, and the balance, after setting off 173 A., equally between his two sons. What was the share of each son and daughter?
179. How many yards of carpeting yd. wide will cover a door 18 ft. sq.?