REVIEW PROBLEMS.

176. A right-angled triangle, of which the base and perpendicular are 3 ft. and 4 ft. respectively, is made to turn round on the longer side; find the volume and the whole surface of the cone thus generated.

177. The surface of a certain solid is five times as great as the surface of a similar solid; what is the ratio of their solidities?

178. A rectangular field is 600 yards long and 400 yards wide; what is the length of its diagonal?

179. The perimeter of an isosceles triangle is 153 yards, and each of the equal sides is five-eighths of the third side; what is the area?

180. A cylinder, 10 ft. long and 3 ft. in diameter, is closed at each end by a hemisphere; what is the whole surface of the solid?

181. A cubic foot of iron is expanded by heat so that each face is increased 2% in area; what is the increase in volume?

182. A field contains 1 acre; how many cubic yards of earth will it require to raise the surface of the field 1 foot ?

183. A field in the form of a trapezoid is to be cut into three lots by lines parallel to the parallel sides of the field; what is the width of the lots, if the area of each is 1 acre and the width of the three is 50 yards, the base being 435.6 yd.?

184. The perimeter of one square is 500 in., and the perimeter of another is 380 in.; what is the perimeter of a square which is equal in area to the other two?

185. Find the side of a cube that contains 32768000 cu. rd. 186. Find the diagonal of a square that contains 39204 sq. in., and the area of the inscribed circle.

187. A room is 31 ft. 6 in. long; what is its width, if the area is 84 sq. yd.?

188. The radius of the base of a cylinder is 6 ft., and the height is 15 ft.; what is the volume?

GAUGING.

FIND the contents in gallons of casks having the following dimensions:

189. Head diameter 25 in., bung diameter 28 in.; length 42 inches.

190. Head diameter 26 in., bung diameter 34 in.; length 45 in. 191. Diameters 24 inches and 32 inches; length 42 inches. 192. Diameters 28 inches and 35 inches; length 40 inches. 193. Diameters 25 inches and 30 inches; length 50 inches. 194. Diameters 30 inches and 36 inches; length 42 inches. 195. Diameters 12 inches and 16 inches; length 20 inches. 196. Diameters 25 inches and 33 inches; length 48 inches. 197. A barrel of wine weighs 361 pounds; the empty barrel weighs 100 lb. ; what is the number of gallons in the barrel, if a cubic foot of wine weighs 62 lb.?

BOARD MEASURE.

FIND the number of board feet in each of the pieces of hewn timber whose dimensions are as follows:

198. 30 ft. 10 in. long, 3 ft. 4 in. wide, and 12 in. thick. 199. 75 ft. long, 2 ft. 9 in. wide, and 16 in. thick.

200. 45 ft. 7 in. long, 18 in. wide, and 9 in. thick.

201. 50 ft. long, 8 in. square at one end, and 2 ft. square at the other.

202. 60 ft. 9 in. long, 14 in. by 10 in. at one end, and 7 in. by 5 in. at the other.

Find the number of cubic feet of timber in logs having the following dimensions:

203. Diameters of the ends 4 ft. and 6 ft. respectively; length 20 ft.

204. Diameters of the ends 3 ft. 6 in. and 5 ft. 2 in. respectively; length 26 ft. 8 in.

205. Diameters of the ends 7 ft. and 6 ft. respectively; length 18 ft.

BRICK-WORK.

FIND the number of bricks 8 in. long, 4 in. wide, and 23 in. thick in walls having the following dimensions, the courses of mortar being of an inch in thickness:

206. Length 50 ft., height 40 ft., thickness 171⁄2 in. 207. Length 120 ft., height 54 ft., thickness 13 in. 208. Length 400 ft., height 5 ft., thickness 8 in. 209. Length 75 ft., height 42 ft., thickness 26 in. 210. Length 183 ft., height 30 ft., thickness 13 in. 211. Length 250 ft., height 60 ft., thickness 26 in. How many bricks will be required, of the size given above, in laying pavements of the following dimensions ?

212. 250 feet long and 12 feet wide.

213. 1 mile in length and 10 ft. 6 in. wide.

214. 16 feet long and 9 feet wide.

215. 1 chain 75 links in length and 11.5 links wide.

HAY AND COAL.

How many pounds of hay in stacks whose dimensions are as follows?

216. In a stack of clover hay equal in volume to a cube 10 ft. 6 in. on each side.

217. In a stack of timothy hay 7 × 5 × 3 ft.

218. In a bale of clover hay which measures 41 × 31×17 ft. 219. In a bale 5 × 4 × 34 ft., if a cubic foot weighs 12 lb. 220. How many tons of clover hay can be stored in a space which measures 30 × 20 × 10 feet?

How many tons (2000 lb.) of anthracite coal can be stored in bins having the following dimensions?

221. 12 feet long, 4 feet wide, and 4 feet high.
222. 18 feet long, 12 feet wide, and 5 feet high.

223. 24 feet long, 18 feet wide, and 6 feet high.
224. 10 ft. 6 in. long, 5 ft. 4 in. wide, and 8 ft. high.
225. 16 ft. 4 in. long, 7 ft. wide, and 9 ft. high.

THE METRIC SYSTEM.

1. IN 56 m. 8 dm. 4 cm. 1 mm. how many
2. In 36 Ds. how many decisteres?

millimeters?

3. How many times will a wheel of which the circumfer ence is 3.25 m. turn in a distance of 10 Km.?

4. If a cart-wheel is 19.38 m. in circumference, how many revolutions will it perform in traveling 1257762 Dm.?

5. If the circumference of a hoop is 7.438 m., how many minutes will it take to pass over 26033 m., supposing it to turn 100 times a minute?

6. What was the speed per hour of a train which traveled 192132.35 m. in 3.65 hours?

7. Two men, A and B, began to walk together, and continued walking for 5.47 hours. A walked 6.39 Km. per hour, while B walked 5.68 Km. per hour; how many meters was B behind when they stopped?

8. If a square kilometer of land is worth $1400, how much is a square hektometer worth?

9. A square contains 289000000 a.; express in millimeters the sum of the lengths of its four sides.

10. How many steres in a room 49.38 m. long, 14.25 m. wide, and 1.5 Dm. high?

11. A merchant buys 8750 steres of wood, for one-half of which he pays 12 francs 75 centimes a stere, and for the other half 15 francs 25 centimes a stere; the measuring costs him 20 centimes a stere; how much does he gain or lose by selling it at 14 francs 10 centimes a stere?

12. A tank, 7.6 m. long and 4.9 m. wide, contains 130340 1. of water when full; how deep is the tank?

13. How many more liters are contained in a tank 30.8 dm. long, 21 m. deep, and 13.6 dm. wide than in one whose cubic contents are 4 steres?

14. A cistern contains 9 Hl. 9 dl. 9 cl. of water; in what time will it be emptied by a pipe which discharges 141 cl. in a minute? In what time will it be filled again by another pipe which pours in 213 cl. in a minute?

15. What would be the cost of papering a room 45 m. square and 18 m. high with paper costing 2.98 francs a square meter?

16. What is the weight in kilos of a cubic centimeter of gold, if 7 cubic decimeters weigh 135.5319 kilos?

17. The height of a table is of its length; what is this height, if the length is of 3.43 m.?

18. If a man earns 6 francs a day, and his son earns 3 francs 75 centimes a day, how long will it take them to save 31 francs, if their united expenses amount to 5 francs a day?

19. A brick wall is to be built 30 m. long, 18 m. high, and 73 cm. thick. How many bricks will be required, if each brick contains 1460 cubic centimeters?

20. A man walks 3 Km. 654 m. in 42 minutes; what is his hour?

rate per

21. If 1 horse eats as much grass as two cows, how many days will a field of 736 Ha. support 83 horses, if 74 cows require 247 Ha. for 13 days?

22. Divide 719.6 francs among 4 men, 5 women, and 6 children, giving to each man three times as much as to each woman, and to each child half as much as to each woman.

23. How many napoleons, five-franc pieces, francs, halffrancs, and sous are there in 4072 francs 45 centimes, there being an equal number of each of the first two coins, and half that number of each of the last three coins?

24. If 6 horses eat in 4 days 144 Kg. 96 g. of hay, how long will 675 Kg. 450 g. last 15 horses?

25. What number of square flag-stones, each 2 dm. 40 mm.