15. How many square yards in the above circle?

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 feet 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. radius?

What is its

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

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. by 12 in., 16 ft. long, at $25 per M.

VOLUMES.

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

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

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

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

185. The Volume or Solidity of a body is the number of cubic 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 in. 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.

2. Find the number of cubic feet of air in a school

room 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 cu. 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 cu. ft. 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 eu. ft.?

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. 10 in. long, 214 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

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 Ex. 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?

18. How many cubic inches of water will the 2 doz. cans (Ex. 17) contain?

19. What will it cost to dig a cellar 36 ft. long, 24 ft. wide, and 6 ft. deep, at 20 cts. a cubic yard?

WOOD MEASURE,

187. A pile of wood 8 feet long, 4 feet wide, and 4 feet high makes a Cord.

One of the 8 feet in length of a cord of wood is a Cord Foot.

NOTE. of equal size.

This may be illustrated by placing side by side 8 books
One of the books represents a cord foot.

How many cords of wood in the following:
1. A pile 18 ft. long, 4 ft. wide, 8 ft. high?
2. A pile 50 ft. long, 8 ft. wide, 6 ft. high?
3. A pile 19 ft. long, 2 ft. wide, 54 ft. high?
4. A pile 16 ft. long, 4 ft. wide, 7 ft. high?

5. What is the cost of a pile of wood 10 ft. long, 4 ft. wide, and 8 ft. high, at $44 a cord ?

6. How high must a pile of wood be piled to contain 10 cords, if the pile is 50 ft. long?

7. How many cords of wood can be piled in a shed 24 ft. long, 18 ft. wide, and 12 ft. high?

8. How many cords of building-stone in a pile 18 ft. long, 6 ft. wide, and 3 ft. high?

9. At $3.50 a cord, what will be the cost of a pile of stone 15 ft. long, 4 ft. wide, and 5 ft. high?

10. How many cubic feet in a cord of 2-foot wood? 3-foot wood? 18-inch wood?

CAPACITY OF BINS.

188. 1. A bushel fills 2150.42 cubic inches of space. How many bushels of wheat can be contained in a bin 5 ft. X 5 ft. x 4 ft. ?

5 × 5 × 4 × 1728 ÷ 2150.42.

NOTE. A bushel fills 1 cu. ft. of space nearly.

-

How

2. A wine gallon fills 231 cubic inches of space. many gallons of water can be contained in a rectangular tank 10 ft. by 8 ft. by 4 ft.?

=

NOTE. -A cubic foot of space contains 1728 gal. 7 gal. nearly.

Find the contents in bushels:

3. Of a bin 6 ft. long, 5 ft. wide, and 4 ft. high.

4. Of a wagon-box 10 ft. long, 42 in. wide, and 22 in. high.

5. Of a box 3 ft. by 24 ft. by 24 ft.

6. How high must a bin 8 ft. long and 5 ft. wide be built to contain 120 bushels ?

Find the contents in gallons.

7. Of a tank 8 ft. by 6 ft. by 24 ft.

8. Of a cistern 6 ft. by 5 ft. by 4 ft.

9. Of a tank 5 ft. square and 6 ft. deep.

10. How many barrels of water will a cistern contain that is 6 ft. by 6 ft. by 7 ft. ?

11. A circular cistern is 5 ft. in diameter and 6 ft. deep. How many barrels of water will it hold?

12. How deep must I build a bin that is 6 ft. square, to hold 90 bushels of wheat?

13. How deep must I build a tank that is 5 ft. square to hold 40 barrels ?