38. Find the cost of papering a room 13m long, 12m wide, and 7m high, with paper 45cm wide and 7.5m in a roll, at $1.50 a roll, put on; and of putting on a border, at $.30 a running meter, allowing 115m for baseboards, doors, etc.

39. Find the cost of plastering this room, at $.60 a square

meter.

BOARD MEASURE.

209. When boards are 25mm or less in thickness, they are sold by the square meter. Likewise, boards more than 25mm thick, plank and "dimension" lumber are sold by board measure. That is, by calculating the number of square meters of boards 25mm thick to which each piece is equivalent.

Thus, a board 4m long, 25cm wide, and 25mm or less in thickness, is a meter, board measure; but a plank 4m long, 25cm wide, and 75mm thick, is three meters, board measure. For, since the plank is three times as thick as an ordinary board, it is equivalent to three boards, each 4m long and 25cm wide.

If a board tapers regularly, its average width is found by taking one-half the sum of its end widths.

How many meters, board measure:

40. In a board 8m long and 20cm wide?

41. In a joist 5m long, 25cm wide, and 75mm thick? 42. In a stick of timber 15m long and 40cm square ?

43. In 2 joists 5m long, 27.5cm wide, and 50mm thick? 44. In 10 planks, each 4m long, 45cm wide, and 10cm thick? and what is the value of these planks, at $25 a hundred meters?

45. In 25 box boards, each 4m long, 42cm wide, and 20mm thick? and what is their value, at $14 a hundred meters?

Find the cost of:

46. Ten joists 4.5m long, 10cm wide, and 7.5cm thick, at $11 a hundred meters.

47. Thirty-six planks, each 4m long, 27.8cm wide, and 75mm thick, at $16 a hundred meters.

48. Three sticks of timber, each 8m long, 22.5cm wide, and 20cm thick, at $17.50 a hundred meters.

49. A board 8.25m long, 28cm wide at one end and 35cm at the other, and 31.25mm thick, at $.30 a meter?

50. A stick of timber 10m long, 25cm thick, 30cm wide at one end and 25cm wide at the other, at $14 a hundred

meters.

51. The flooring for a two-story building 16m by 10.5m; the flooring being 32mm thick, and worth $30 a hundred

meters.

52. The flooring timbers for this building, the timbers being 25cm by 50mm, and placed on edge 30cm apart, and worth $11.50 a hundred meters.

53. The fencing to enclose a field 150m long and 75m wide; the posts are set 2.5m apart, and cost $.25 apiece; the fence is 5 boards high; the bottom board is 30cm, the top board 25cm, and the other three each 22.5cm wide, and the boards cost $13.25 a hundred meters.

NOTE. Round logs are sold by board measure; .25 is deducted for slabs. A scale is used, the calipers of which are applied to the middle of the log, and the amount of boards for a given length is read off the scale.

Large and heavy timber is sold by the ton; only 20 is allowed for slabs, and the amount is reckoned in cubic measure instead of board measure.

MEASURES OF VOLUME.

To find the volume of a rectangular solid.

210. In the figure represented in the margin, let the length contain 5, the breadth 3, and the

height 7 linear centimeters.

The base may be divided into square centimeters: there will be three rows of 5 square centimeters each; in all, 15 square centimeters. Upon each square centimeter may be placed a pile of 7 cubic centimeters; so that the solid will

contain 15 x 7 cubic centimeters, that is, 3 x 5 x 7 cubic centimeters. Hence,

Express the length, breadth, and height of a rectangular solid in the same linear unit; the product of these numbers will be its volume in cubic units of the same name as the linear unit of the edges.

EXERCISE VI.

1. How many cubic centimeters in a block 9cm long by 7em wide, and 6cm deep?

2. If wood is cut into 120cm lengths,

and a pile is 43.7m long and
1.4m high, how many sters of
wood are there in it?

3. In a grain elevator is a bin 11.2m
long, 4.34m wide, and 2.83m

deep. How many hektoliters
of grain will it hold?

Hektoliter.

4. If a liter of grain weigh .81 of the weight of a liter of water, how much will the grain in that bin weigh?

5. A bin measuring 16m by 9.7m, and 2.8m deep, is full of oats, worth $.98 a hektoliter. What is the whole

worth?

6. A vat 197cm long, 87cm wide, and 63cm deep, holds how many liters? What would be the weight of water required to fill it?

7. Add 1341ccm, 2311, and 2.13h1, and give the sum in terms of each of the three units.

8. If a spring pours out 467.8' each minute, how many hektoliters will it deliver in 60 minutes? in 37 minutes? in 78 minutes?

9. If 67.31 of oil in a vat with perpendicular sides fill it to a depth of 173mm, how deep will 13.7 times that quantity fill it? and how many hektoliters will there be?

10. Into a round cup 10cm across, with perpendicular sides, pour oil until it is 1em deep; then there are 78.54ccm of oil in the cup. (See § 204.) How many cubic centimeters will there be when the oil is 38mm deep? 11. What is the capacity of a tin cup 95mm across and 11.08cm deep?

12. What are the capacities of two cylindrical vessels, one being 16.24cm across and 19.95cm deep, the other 75.4mm across and 87.9mm deep?

211. The volume of a sphere is found by multiplying the cube of the diameter by .5236.

13. How many cubic centimeters in a ball 10cm in diameter? How much less if you take the more exact multiplier? § 201.

14. Into a cubical box 20cm on a side, and full of water, an

iron ball 20cm in diameter is gently lowered until it touches bottom. How much water is left in the box? Answer in liters and in cubic centimeters.

15. One cask contains 171.41 of oil; another, 209.31; a third, 73.8'; while a square vat, 137cm each way, is filled to

a depth of 69cm. How much oil in all the vessels? in liters and in hektoliters.

16. How many liters of air in a room 7.8m long, 6.23m wide, and 3m high?

17. If a person's breathing spoil the air at the rate of .2175cbm a minute, how long will it take 3 persons sitting in the room, closed, to spoil the air?

18. How long, at the same rate, would the air in a hall 22m long, 16m wide, and 7m high, last an audience of 280

persons?

19. How many cubic meters of wood in a round stick of equal size throughout, 37cm in diameter and 8.4m long?

EXERCISE VII.

1. What is the weight, in kilograms, of a hektoliter of water? of 73.8' of water? of a cubic meter of water? of a cubic centimeter?

2. If a man buys half a ton of potatoes for $20, and retails them all, without waste, at 5 cents a kilogram, what profit does he make on the whole?

3. What is the weight of water required to fill a vat 98cm long, 71cm wide, and 38cm deep?

4. If the vat of the last example were filled with brine weighing 1.04kg to the liter, what would be the weight of the brine?

5. If the vat of Example 3 were filled with wine weighing .981kg to the liter, what would be its weight?

6. What is the total weight of 13 men averaging 73.48kg

each?