Find the areas of the circles whose radii are:

Find the volumes of the pyramids whose bases and alti

Find the volumes of the cones whose altitudes and the

radii of whose bases are respectively :

92. If a cubic foot of granite weighs 165 lb., what is the weight of a sphere of granite 1 ft. in diameter?

93. How many tons of water will fill a tank 14 ft. by 8 ft. by 8 ft., allowing 1000 oz. to a cubic foot?

94. A bowl is in the form of a hemisphere 4.2 in. in diameter. How many cubic inches does it contain?

95. If a cubic foot of marble weighs 173 lb., what is the weight of a cylindrical marble column 10 ft. high and 16 in. in diameter?

96. How many loads (cubic yards) of earth must be removed in digging a canal 2 mi. 1740 ft. long, 200 ft. wide, and 16 ft. deep?

97. In a cylindrical jar 4 in. high and 3 in. in diameter, half full of water, a marble 1 in. in diameter is dropped. It causes the water to rise how much?

98. What is the weight of a sphere of steel 7 in. in diameter, steel being 7.8 times as heavy as water, and 1 cu. ft. of water weighing 1000 oz.?

99. What is the weight of a sphere of marble 3 ft. in circumference, marble being 2.7 times as heavy as water, 1 cu. ft. of water weighing 1000 oz.?

100. The entire surface of a pyramid is made up of four equal-sided triangles 3 ft. on a side. What is the total area? (Carry the result to hundredths.)

101. The diameter of a sphere and the altitude of a cone are equal, and they have equal radii. The volume of the sphere is how many times that of the cone?

102. Taking the radius of the earth as 4000 mi., and the earth as an exact sphere, what is its volume? How many square miles on its surface? (Carry the answers only to 1000 square or cubic miles.)

MISCELLANEOUS PROBLEMS

296. Nature of the problems. The following list contains certain problems whose interest is rather in the reasoning exercised in solution than in their applicability to the life of to-day.

WRITTEN EXERCISE

1. Divide 91 into two parts having the ratio of 5:8. 2. The product of two numbers is 175 and their quotient is 7. What are the numbers?

3. How many bananas are there in a bunch of which 7 are decayed and 95% are not?

4. The sum of two numbers is 783 and their difference is 191. What are the numbers?

5. At 200 lb. per cubic foot, what is the weight of a block of stone 4′31′′ × 1′ 1′′ × 9.6"?

6. At $1.95 a rod, how much will it cost to fence a rectangular 2-acre field that is 5 ch. long?

7. If iron weighs 444.56 lb. per cubic foot, find the weight of a 14-ft. bar of 2" × 11′′ iron.

8. How much is gained by buying 63 gal. of molasses for $25.20 and selling it at 12 a quart?

9. What is the rate of gain when oranges are bought at 40 for $1, and sold at 50g a dozen?

10. What is the rate of gain when eggs are bought at 16 for a quarter and sold at 13 for a quarter?

11. What is the height of a block of marble 4' 2" x 2'1", that weighs as much as one 3′ 4′′ × 2′ 1′′ × 2' 5"?

12. A man owns 100 A. of coal land, the coal bed being 11 ft. thick. Allowing 35 cu. ft. to the ton, how many tons of coal in the bed?

13. The minute hand of my watch is in. long. Over what area does it pass in a day?

14. If 15 horses eat 11 bu. of oats in 9 da., how long will 44 bu. last 45 horses at the same rate?

15. In the year when Michigan produced 11,135,215 long tons of iron, how many pounds did it produce?

16. If telegraph poles are 198 ft. apart, and a train passes one every 3 sec., what is the train's rate per hour?

17. The pitch of a screw is 16 threads to the inch. How many turns must be made to move the screw in.?

18. A dealer bought hay at $8.66 a ton and sold it at $9.75, gaining $408.75. How many tons did he buy?

19. What will it cost to fill in 3 acres of swamp land, raising the level on an average of 5 ft., at 45¢ a load?

20. A man used a bicycle for a month and sold it 15% below cost, receiving $29.75 for it. How much did he lose? 21. What is the list price of some goods which cost $68.40 after the discounts 10%, 5% have been deducted?

22. At what price must a dealer mark goods that cost him $450 so as to take off 10% and still make 10% profit?

23. What is the shortest distance that can be measured exactly by a yardstick, a fathom rod, or a pole 1 rd. long?

24. A man sold two carriages at $150 each. On one he gained 20%, and on the other he lost 20%. Did he gain or lose on both, and how much?

25. A man bought a horse for $95 and sold it for $114. What was his gain per cent? The purchaser sold the horse for $95. What was his loss per cent?

26. In the year when Michigan produced 7,729,808 barrels of salt, this was 37.6% of the total amount produced in the United States. How many were produced in all?

27. At what distance from the end must a piece of timber 16" square be sawed so as to cut off 9 cu. ft.?

28. Around a circular flower bed 28 ft. in diameter is a gravel walk 7 ft. wide. What is the area of the walk?

29. If 6 men can do a piece of work in 4 da., how many more must be employed to finish the work one day sooner?

30. A man can mow of a field in 12 hr. How many hours will it take to mow the whole field at this rate?

31. If 84 men can do a piece of work in 2 mo., how long will it take 12 men to do the same work at the same rate?

32. A train 156 ft. long is traveling 60 mi. an hour. How long will it take it to completely cross a bridge 295 ft. long?

33. One man can do a piece of work in 4 da. which another can do in 5 da. At these rates, how long will it take them to do the work together?

The first does what part in one day? The second does what part in one day? Together they do what part in one day? How many days will it take them?

34. A boy, after doing of a piece of work in 30 days, is assisted by a man, with whom he completes it in 6 days. How long would it take each to do the work alone?

35. If a certain number of men can do a piece of work in 15 da., how long will it take if twice as many men are added to this number?

36. If 19 men can do a piece of work in 76 da. of 7 hr. each, how many men, working at the same rate, will it take to do the work in 133 hr.?

37. An expert typesetter, working by the hour, receives $32.40 a week, working 9 hr. daily except Sunday. How many hours a day must he work to earn $19.20 in 4 da. at the same rate?