ORAL EXERCISE

In Exs. 1–12, x represents a missing number. What is

13. If the product of three numbers is 400, and two of the numbers are 5 and 10, what is the third one?

14. If the product of three numbers is 540, and the product of two of them is 90, what is the third number?

15. If a box is 9 in. by 10 in. by 11 in., what is its cubic contents? If the cubic contents of a box 9 in. wide and 11 in. long is 99 cu. in., how deep is the box?

16. If a box contains 54 cu. in., and is 9 in. long and 3 in. wide, how deep is it?

17. If a box contains 24 cu. in., and the area of the base is 6 sq. in., how deep is the box?

Given the following volumes of boxes, and the length and breadth, find the depth:

51. Illustrative problems. 1. How thick is a block 5 ft. long and 4 ft. wide, containing 60 cu. ft.?

Analysis:

If it is x ft. thick, x times 5 times 4 cu. ft.

Work:

60

fore it is 3 ft. thick.

We may, if we prefer, give this analysis :

Since it is 5 ft. long and 4 ft. wide, the area of the base is 20 sq. ft.

If it were 1 ft. high, the volume would be 20 cu. ft.

Therefore it is as many times 1 ft. high as 60 cu. ft. ÷ 20 cu. ft., or 3.

52. Hence we see that

The number of cubic units of volume, divided by the product of the numbers of units of two dimensions, equals the number of units of the third dimension.

This is sometimes less accurately expressed: The volume divided by two dimensions equals the third dimension.

2. What is the area of the base of a block 21⁄2 in. high, containing 70 cu. in. ?

If it were 1 in. high, the volume would be 70 cu. in. 2 = 28 cu. in. But the base of such a block is 28 sq. in.

5

70 ÷

2

2 × 70

- : 28

5

This might be briefly stated as in § 52: The volume divided by the height equals the area of the base. This has a meaning only as

we think of the measures as abstract numbers.

3. What is the thickness of a block containing 100 cu. in., the base containing 30 sq. in.?

100

If it were 1 in. thick, it would contain 30 cu. in.

30

Therefore it is as many times 1 in. thick as

100 cu. in. ÷ 30 cu. in. 3. Therefore it is 3 in. thick.

WRITTEN EXERCISE

How deep is it?

1. How many cubic feet in a hall 80' × 60' × 23' 4"? 2. A tank 9' x 16' contains 900 cu. ft. 3. A box 13" x 20" contains 3900 cu. in. 4. A tank 4' deep contains 450 cu. ft. of the base?

How deep is it? What is the area

5. A hall 22' high and 30' wide contains 28,600 cu. ft. Find the length.

6. A block containing 700 cu. ft. has a base area of 56 sq. ft. How thick is it?

7. A hall contains 41,341.3 cu. ft. It is 41.3 ft. long and 36.4 ft. wide. How high is it?

8. A box contains 42.159 cu. in. The area of the bottom is 10.81 sq. in. How deep is the box?

9. A block of granite is 14 in. long and 8.3 in. wide. It contains 836.64 cu. in. How thick is it?

10. The floor of a hall contains 1386 sq. ft. The hall contains 15,246 cu. ft. Required the height.

11. A storeroom is 14.3 ft. long, 13 ft. 6 in. wide, and has a capacity of 2316.6 cu. ft. How high is the room?

12. The floor of a room is square and contains 144 sq. ft. The room contains 1368 cu. ft. Required the three dimensions of the room.

13. A room 24 ft. long and 9 ft. high, containing 3240 cu. ft., is carpeted with plain ingrain carpet 1 yd. wide. What is the cost of the carpet at 759 a yard?

14. A room contains 2110.68 cu. ft. The room is 16.4 ft. long, and the floor area is 234.52 sq. ft. What are the three dimensions of the room?

15. Express in bushels the volume of a bin 6 ft. by 4 ft. by 3 ft. 6 in., allowing 2150 cu. in. to the bushel.

16. How many bars of soap, each 4 in. long, 23 in. wide, and 1 in. thick, can be packed in a box 16 in. long, 133 in. wide, and 1 ft. deep?

17. What is the value of the bricks in a kiln 60 ft. long, 25 ft. wide, and 9 ft. high, each brick being 8 in. by 4 in. by 2 in., at $9 a thousand?

18. The length of a tank is 100% greater than its width, and its width is 200% of its depth. If the width is 2 yd., how many gallons does it hold?

19. A cord of stone having the same volume as a cord of wood, what is a pile of stones 27 ft. long, 5 ft. wide, and 6 ft. high worth at $4.20 a cord?

20. If it takes 550 cu. ft. of clover hay to make a ton, how many tons will fill a mow 32 ft. long, the width being double the depth and half the length?

21. Allowing 231 cu. in. to the gallon, how many gallons in a watering trough that is 6 ft. long and 16 in. wide, the ratio of its depth to its width being 3: 4?

22. A bin 21 ft. 6 in. long and 10 ft. wide is filled with wheat to the depth of 5 ft. Allowing 2150 cu. in. to the bushel, what is the wheat worth at 80g a bushel?

23. Find the cost of the carpet needed for a room 11 ft. 3 in. wide, 10 ft. high, containing 2278 cu. ft. 216 cu. in., the carpet being 27 in. wide and costing $1.35 a yard, allowing 9 in. for matching on each strip except the first.

24. A cellar is 32 ft. long, 17 ft. wide, and 8 ft. 6 in. deep. How much will it cost to build the wall, 1 ft. thick, at 35 per cubic foot, no allowance being made for openings, and the length of the wall being determined by the outside measure (thus doubling the corners)?

LONGITUDE AND TIME

53. Axes. A point on any surface may be located by two

measures taken from two inter

secting lines XX' (read "XX prime") and YY. These lines are called axes.

In this figure the point A is 2, 1, and the point B is 5, 2.

Distances to the left of YY', or below XX', may be marked -.

Thus, C is 2, 3, and D is – 1, − 2.

X

Y

B

54. Prime meridian. An arc on the earth's surface, from the north pole to the south pole, is called a meridian. The one through the Royal Observatory at Greenwich, England, is taken by most nations as the prime meridian.

55. Points on a map. On a map the lines taken for locating points are the equator and the prime meridian.

56. Latitude and longitude. Instead of giving the distances from these lines in miles, they are given in degrees. Thus, St. Louis is located when we say that it is 90° 12′ 17′′ W., 38° 38' 3.6" N. The distance in degrees east and west from the prime meridian is called longitude; north and south from the equator, latitude.

WRITTEN EXERCISE

1. Draw two axes and indicate the points 2, 4; 7, 6.

3. In the same way, indicate the points -2, -3; −1, −4.

4. In the same way, indicate the points 3,

2; 2,

1

5. Draw a rough map, indicating a place 40° N., 75° W.