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Exercise

1. How much 2-in. rope can be wound on a reel with the dimensions given in the figure ?

2. How much 1-in. garden hose can be wound on the reel of Ex. 1 ? How much k-in. carpenters' chalkline?

0 16"

24" 3. How much wire .05 in. in diameter can be wound on a reel 11 in. in diameter over all, with a shank 6 in. in diameter and 6 in. long? How much wire if the diameter is twice as great ?

4. If the tire of a cart wheel is lengthened 2 feet, how much clearance will there be ?

5. How many feet of 4-in. wire cable will a reel hold if it has a shank 4 ft. long, 1 ft. in diameter, and a 3-in. flange ?

6. If a captive balloon is held by a wire cable i in. in diameter which weighs .1 lb. per foot and has a tensile strength of 2400 lb., how high can the balloon be allowed to go without danger of the cable's breaking of its own weight?

7. What must be the inside dimensions of a cubical box which will hold 8000 quarter-inch buckshot?

8. If the 8000 buckshot of Ex. 7 are melted and recast in the form of a cylinder whose diameter and height are equal, what is its diameter and height if a 5 per cent allowance is made for waste in melting?

9. If the cylinder of Ex. 8 is melted and recast in the form of cubical blocks 1 in. on each edge, how many can be made, allowing 5 per cent for waste ?

10. Determine the weight per foot of lead pipe 2 in. in diameter and { in. thick. (A cubic foot of lead weighs 710 lb.)

11. What must be the depth of a 5-gallon pail the diameter of whose top is 14 in. and whose base is 9 in. ?

12. To what depth will the pail of Ex. 11 be filled when it holds 4 gallons ? To what depth when it holds 3 gallons ?

13. A pail is 8 in. in diameter at the top, 6 in. in diameter at the bottom, and 7 in. deep. Where on the side must it be marked to indicate 1 qt. ? 2 qt. ? 3 qt. ?

14. A cylindrical tank is 4 ft. long and 2 ft. 6 in. in diameter, inside dimensions. When it stands on end the water in it is 18 in. deep. How deep will the water be when the cylinder is lying on its side? (See below.)

15. A certain cubical tank will hold 216 cu. ft. T T h of water. What must be

_L the dimensions of a simiCIRCULAR SEGMENT

larly shaped tank which

will hold 300 gallons ? The area of a circular segment can be found by the formula

d

A=

where

4 h2 d

0.608
3 h
A = area
d = diameter of circle
h = height of segment

16. Using the formula just given, find the area of the segment if d = 16 inches and h = 6 inches.

The contents of a partially filled horizontal cylindrical tank can be computed from the formula

ld
C=.005772 h?1 0.608

h where

C = contents in gallons
d = diameter in inches
h = depth of liquid in inches

l= length of tank in inches 17. Find the number of gallons of liquid in a horizontal cylindrical tank 6 feet long, 16 inches in diameter, if filled to a depth of 6 inches.

CHAPTER XV

MISCELLANEOUS PROBLEMS

1. A man who owned ã of the stock in a certain company sold of what he owned. What part of the company stock did he then own ?

2. An automobile is bought for $ 1600, run for 4 years and sold for $ 750. During that time the cost for gasoline and oil averaged $.75 a day; repairs, including tire expense, amounted to about $ 25 a month ; license $15 a year; and insurance $ 25 a year. What did the automobile cost per day?

3. A map of Kansas is made on a scale of 1 inch to 100 miles. The map measures 4 inches by 2 inches. Find from it the area of the state.

4. If a circus ring is 42 feet in diameter and a horse makes 23 lopes in going round it, how far does the horse go in each lope ? Assume that the path of the horse is 6 inches inside the rim.

5. Prepare a diagram setting forth graphically the following facts. Of the persons who have attained sufficient distinction to be listed in “Who's Who in America" 71% were college trained ; 16% had high school training ; 9% stopped after the grammar school; 3.8 % were prepared by private tutors; and .2 % are self-made.

6. A tank 8 feet 3 inches long, 3 feet 6 inches wide, and 4 feet 6 inches deep is ž full of water. How many gallons are there in the tank ?

7. How many board feet are there in a stick of timber 18 feet long, 16 inches wide, and 12 inches thick ?

8. What is the cost of a casting weighing 240 pounds at 61 cents a pound ?

9. The side of a square is 100 feet. Find the length of a diagonal.

10. Divide 60 into two parts in the ratio of 2 to 3.

11. What per cent of 3 inches is i of an inch, of an inch, ki?

12. How many feet of wire will be required to fence (three wires) a 12-acre field if it is square? How many if it is twice as long as it is wide ?

13. What is the value of a ton of silver dollars at $ 1.30 an ounce if each dollar weighs 4121 grains ?

14. If pocket knives are worth $21 a dozen, what is the price per knife ?

15. On a map made on a scale of 6 inches to a mile, a rectangular field is represented by a space 1 inch long and I of an inch wide. How many acres are there in the field ?

16. A machinist receiving $ 6.25 per day is given a 10 per cent increase. Later he is cut 10 per cent.

What is his wage then ? Why is it not the same as it was before the increase ?

17. Find the cost of making a driveway 200 yards in length and 8 yards wide, the soil being first excavated to a depth of 14 inches at a cost of 25 cents per cubic yard; crushed stone then being put in 8 inches deep at a cost of 30 cents per cubic yard, and gravel placed on top 6 inches deep at a cost of 50 cents per cubic yard.

18. If lubricating oil can be bought at 22 cents a quart, how many gallons will $5 buy?

19. Divide 66 into parts proportional to 2, 3, and 4.

20. How many 5-ounce bottles can be filled from 5 gallons of liquid ?

21. What is the weight of $1,000,000 in silver if one dollar weighs 412į grains ?

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