6. How many feet of lumber will it take to build a line fence 168 ft. long, the fence being 5 boards high, and the boards 6 in. wide?

7. What will be the cost of 10 planks, each 12 ft. long, 10 in. wide, and 3 in. thick, at $16 per M. ?

8. Find the cost of a stick of timber 8 in. square, and 40 ft. long, at $18 per M.

9. What is the cost of 8 sticks of timber each 36 ft. long, 10 in. wide, 8 in. thick, at $12 per M.?

10. How many board feet of 2-inch planking will it take to make a walk 4 feet long and 3 feet wide?

11. Find the cost of 7 planks 12 ft. long, 16 in. wide at one end, and 12 in. at the other, at $.08 a board foot.

12. At $18 per M., find the cost of flooring a room 21 ft. by 16 ft., allowing of the lumber for matching.

NOTE. Find area of floor and add }.

13. Find the cost of a board 20 ft. long, 22 in. wide at one end, and tapering to 16 in. at the other, and 1 in. thick, at $30 per M.?

14. At $12 per M., what will be the cost of 2-inch plank for a 3 ft. 6 in. sidewalk on the street side of a rectangular corner lot 56 ft. by 106 ft. 6 in. ?

MISCELLANEOUS.

239. 1. My dining-room is 15 ft. long and 12 ft. wide; the walls are 10 ft. high. What will it cost to paper the walls and ceiling with paper 1 ft. wide, if there are 8 yd. in a roll, and each roll costs $.37. (allowed for openings.)

2. What will a carpet for the dining-room (Ex. 1) cost me at $.75 a yd., carpet & yd. wide?

What

3. There are three windows in the dining-room. will it cost to furnish them with shades at $1.10 each and sash-curtains at $1.37 each?

4. I bought a table at $14.50, six chairs at $2.75 each, a sideboard for $30, and other furniture for $28.97. I also spent $20 for new table linen. What did it all cost?

5. What was the entire cost of refurnishing my diningroom? (Ex. 1, 2, 3, 4.)

6. What will it cost to carpet a room which is 24 ft. long, and 18 ft. wide, with Brussels carpet 1 yd. wide, no waste in matching, at $1 per yard?

7. Find the cost of plastering sides and ceiling of a room 26 ft. long, 13 ft. wide, 13 ft. high, at 9 cents a square yard, allowing 25 sq. yd. for openings.

8. What will it cost to build a cement walk 40 ft. long and 6 ft. wide, at $1.25 per square yard?

9. A field, containing 8 acres, is 60 rd. long. How wide is it?

10. How many yards of carpet will cover a floor 18 ft. long, 16 ft. wide? Carpet one yard wide, strips to run lengthwise of room.

How many yards if the strips run crosswise of the room?

11. Find the cost of fencing a rectangular corner lot 68 ft. by 130 ft., the street fence costing 54 cts. a yard, and the line fences 25 cents a yard, but only half of the cost of the latter to be charged to the lot.

12. Find the cost of a carpet & of a yd. wide, at $1.50 per lineal yard, for a room 20 ft. long and 18 ft. wide, strips running lengthwise, and allowing a waste of of a yard on each strip for matching.

13. What is the breadth of a rectangular lot whose area is 75 sq. ch. and the length 9 ch. ?

14. What is the circumference of a circle whose radius is 9 ft.?

15. How many square yards in the above circle? (Ex. 15.) 16. How many revolutions does the 5-foot driving-wheel of a locomotive make in going 30 miles?

17. Find the area of a triangle whose base is 5 ft. and altitude 3 ft.

18. If the circumference of the earth is 25000 miles, what is the diameter ?

19. The circumference of a circle is 18 ft. What is its radius?

20. How many square yards in a triangle whose base is 48 ft. and whose altitude is 24 ft. ?

21. Find the area of the gable-end of a house whose width is 25 feet and whose ridge is 10 feet 6 inches higher than the base of the gable.

22. If the diameter of the earth is 8000 miles, what is the circumference?

23. How many board feet in 10 planks 18 ft. long, 15 in. wide, and 2 in. thick, and what will they cost at $40 per M.?

24. Find the cost of 10 joists, 3 in. bv 12 in., 16 ft. long, at $25 per M.?

VOLUMES.

240. Anything that has length, breadth, and thickness is called a Solid or Volume.

241. A Rectangular Volume is a solid having six rectangular faces.

242. A Cube is a solid having six equal square faces.

243. A Cubic Inch is a cube 1 inch long, 1 inch wide, and 1 inch thick.

244. The Volume or Solidity of a body is the number of eubic units that it contains.

1. How many cubic inches in a block 4 in. long, 3 in. wide, and 2 in. thick?

The block is made up of two layers, each 1 inch thick. In the top layer there are 4 times 3 cu. in. In the two layers, therefore, there are 2 × (4 × 3 cu. in.) = 24 cu. inches.

245. Length x breadth x thickness Solidity.

Solidity

two.

Solidity

=

either dimension the product of the other

=

the product of two dimensions the other.

=

2. Find the number of cubic feet of air in a schoolroom 32 ft. square and 12 ft. high.

3. How high is a room that is 24 ft. long, 20 ft. wide, and contains 4410 cu. ft.?

4. A cubic foot of ice weighs 56 pounds. How much will a load of 22 cakes weigh, each cake measuring 2 ft. square and 1 ft. thick?

5. The capacity of a rectangular box is 480 cu. in. The box is 8 in. wide and 5 in. deep. How long is it?

6. A schoolroom is 25 ft. long, 18 ft. wide, and 12 ft. high. If 60 pupils are seated in it, how many cubic feet of air are allowed for each child?

7. A man sold 3 blocks of Vermont marble, each 8 ft. long, and 6 in. x 6 in. at the ends. How much did he receive for the marble at $ 3.50 per cubic foot?

8. A hot-house bed is 3 ft. 9 in. long, and 3 ft. 4 in. wide, inside measure. How deep must it be to contain 25 cu. ft. of earth, and allow 6 in. for the growth of the plants?

9. How many bricks 8 in. by 4 in. and 2 in. thick will be needed for a wall 60 ft. long, 20 ft. high, and 2 ft. thick, making no allowance for mortar?

10. How many rectangular blocks 12 in. by 8 in. by 3 in. can be packed into a wagon-box 10 ft. long, 4 ft. wide, and 2 ft. 6 in. deep?

11. How many cubic yards of earth must be excavated from a cellar 30 ft. long, 21 ft. wide, and 5 ft. 8 in. deep?

12. How many square feet in the surface of a rectangular box 3 ft. 4 in. long, 2 ft. 2 in. wide, and 14 ft. high?

13. How many cubes 2 inches on each edge can be sawed from a block of marble 10 ft. 2 in. long, 6 ft. 5 in. wide, and 3 ft. 4 in. thick?

14. A box is 1.5 in. long, .85 in. wide, and .58 in. deep. What is its capacity in cubic inches?

15. The altitude of a cylinder is 8 ft. and the circumference of the base is 3 ft. What are the cubic contents of the cylinder?

NOTES.Contents of a cylinder

Area of Base × Altitude.
Area of curved surface of a cylinder

Base x Altitude.

Circumference of

This may be seen by cutting a piece of paper so that it will exactly cover the curved surface of a small cylinder.

16. What is the area of the curved surface in the cylinder mentioned in Example 15?

17. How much tin will be required to make 2 doz. cylindrical shaped cans, with a diameter of 4 in. and altitude of 7 in., allowing tin for the curved surface and the two circular ends?