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2. What is the solidity of a cone the diameter of whose base is 18 and the altitude 27? Ans. 2290,2264.

3. What is the solid content of a cone the diameter of whose base is 20 and the altitude 30? Ans. 3141,6.

4. What is the solidity of a cone whose altitude is 27 feet, and the diameter of the base 10 feet? Ans. 706,86.

5. What is the solidity of a cone whose altitude is 12 feet, and the diameter of its base 15 feet? Ans. 706,86.

§ 207. To find the solidity of a pyramid-Multiply the area of the base by the altitude and divide the product by 3.

EXAMPLES.

*1. Required the solidity of a pyramid of which the area of the base is 95, and the altitude 15.

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2. What is the solidity of a pyramid, the area of whose base is 260 and the altitude 24?

Ans. 2080.

3. What is the solidity of a pyramid, the area of whose base is 207 and altitude 18? Ans. 1242.

4. What is the solidity of a pyramid, the area of whose base is 403 and altitude 30? Ans. 4030.

5. What is the solid content of a pyramid, the area of whose base is 270 and altitude 16? Ans. 1440.

6. A pyramid has a rectangular base, the sides of which are 25 and 12; the altitude of the pyramid is 36; what is its solid content? Ans. 3600. 7. A pyramid with a square base of which each side is 30, has an altitude of 20: what is its solid content?

Ans. 6000.

PROMISCUOUS QUESTIONS.

1. A merchant bought 13 packages of goods, for which he paid $326: what will 39 packages cost at the same rate? Ans. $978.

2. Two merchants, A and B traded together; A put in £320 for 5 months, and B £460 for 3 months; they gained £100: how much should each one receive?

Ans. A £53 13s 9270d, B £46 6s 2,28d. 3. If I buy 1000 Ells Flemish of linen, for £90, what must it be sold for per Ell English, to make £10 by the purchase? Ans. 3s 4d. 4. What number taken from the square of 54 will leave 19 times 46 ? Ans. 2042. 5. If of a gallon of wine cost of a £, what will 5 of a tun cost? Ans. £105. 6. If an officer's salary is £48 per annum, how much will he receive in 232 days? Ans. £30 10s 21d+.

7. If a gentleman spends one day with another, £1 7s 101d, and at the end of the year has saved £340, what is his yearly income? Ans. £848 14s 41d.

8. If 8 cannons expend, in one day, 48 barrels of powder, how much will 24 cannons expend in 22 days? Ans. 3168bar.

9. What number is that which being multiplied by will produce ? Ans..

10. A person dying divided his property between his widow and his four sons: to his widow he gave $1780, and to each of his sons $1250: he had been 25 years in business, and had cleared on an average $126 a year: how much had he when he began business?

Ans. $3567.

11. A besieged garrison consisting of 360 men was provisioned for 6 months, but hearing of no relief at the end of 5 months, dismissed so many of the garrison that the remaining provision lasted 5 months: how many men were sent away? Ans. 288.

12. What number added to 115, will produce 36317? Ans. 24818.

13. What number multiplied by, will produce 11? Ans. 26.

14. A man had 12 sons, the youngest was 3 years old and the eldest 58, and their ages increased in arithmetical progression: what was the common difference of their ages? Ans. 5 years.

15. A snail in getting up a pole, 20 feet high, was observed to climb up 8 feet every day, but to descend 4 feet every night: in what time did he reach the top of the pole? Ans. 4 days.

16. Two persons, A and B are indebted to C; A owes $2173, which is the least debt, and the difference of the debts is $371: what is B's debt? Ans. $2544.

17. What is the difference between twice four and forty, and twice forty-four: also between twice five and fifty, and twice fifty-five? Ans. 40 and 50.

18. A lady being asked her age, and not wishing to give a direct answer, said, I have 9 children, and three years elapsed between the birth of each of them; the eldest was born when I was 19 years old, and the youngest is now exactly 19 what was her age? Ans. 62 years.

19. What number added to the 43d part of 4429, will make the sum 240? Ans. 137. 20. A man went to sea at 17 years of age; 8 years after he had a son born, who lived 46 years, and died before his father: after which the father lived twice twenty years and died what was the age of the father?

Ans. 111 years.

21. A brigade of horse consisting of 384 men, is to be formed into a solid body consisting of 32 men in front; how many ranks will there be? Ans. 12.

22. A room 30 feet long and 18 feet. wide is to be covered with painted cloth of a yard in width: how many yards will cover it? Ans. 80.

23. A, B and C trade together and gain '$120, which is to be shared according to each one's stock; A put in

$140, B $300, and C $160; what is each man's share? Ans. A's $28, B's $60, and C's 32.

24 There is a stone which measures 4 feet 6 inches long, 2 feet 9 inches broad, and 5 feet 4 inches deep: how many solid feet does it contain? Ans. 66 feet.

25. Two men depart from the same place and travel in different directions; one goes 7 miles and the other 11 miles per day: how far will they be apart at the end of the 12th day? Ans. 216 miles. 26. How many planks 15 feet long and 15 inches wide, will floor a barn 60 feet long and 33 feet wide?

Ans. 108

27. A person owned & of a mine, and sold of his interest for $1710: what was the value of the entire mine? Ans. $3800.

28. The swiftest velocity of a cannon ball, is about 2000 feet in a second of time. In what time, at that rate, would it be in moving from the earth to the sun, admitting the distance to be 95 millions of miles, and the year to contain 365 days 6 hours. Ans. 71315 years.

29. The slow or parade step is 70 paces per minute, at 28 inches each pace: how fast is that per hour?

Ans. 1

miles.

30. A wall of 700 yards in length was to be built in 29 days. Twelve men were employed on it for 11 days, and only completed 220 yards. How many men must be added to complete the wall in the required time? Ans. 4.

31. How far will 500 millions of guineas reach, when laid down in a straight line touching one another, supposing each guinea to be an inch in diameter ?

Ans. 7891mi. 728yd. 2ft. 8in. 32. A gentleman whose annual income is £1500, spends 20 guineas a week: does he save or run in debt, and how much? Ans. He saves £408 per annnm.

33. A person bought 160 oranges at 2 for a penny, and 180 more at 3 for a penny; after which he sold them out at the rate of 5 for 2 pence: did he make or lose, and how much? Ans. He lost 4 pence.

34. My factor sends me word that he has bought goods to the value of £500 13s 6d upon my account: what will his commission come to at 3 per cent.?

Ans. £17 10s 51⁄2d+.

35. If a quantity of provisions serves 1500 men 12 weeks, at the rate of 20 ounces a day for each man; how many men will the same provisions maintain for 20 weeks, at the rate of 8 ounces a day for each man?

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Ans. 2250 men.

36. A younger brother received $8400, which was just of his elder brother's fortune: what was the father worth? Ans. $19200. 37. If 20 men can perform a piece of work in 12 days, how many men will accomplish three times as much in one-fifth of the time?

Ans. 300. 38. Suppose that I have of a ship worth $1200; what part have I left after selling of of my share, and what is it worth? Ans. 37 left, worth $986,66+. 39. What number is that which being multiplied by of of 1, the product will be 1?

240

Ans. 11. 40. What number is that which being multiplied by three thousandths, the product will be 2637?

Ans. 879000. 41. What length must be cut off a board 8 inches broad to contain a square foot, or as much as 12 inches in length and 12 in breadth? Ans. 161 inches.

42. A man exchanged 70 bushels of rye, at $0,92 per bushel, for 40 bushels of wheat, at $1,37 per bushel, and received the balance in oats, at $0,40 per bushel: how many bushels of oats did he receive? Ans. 231bu.

43. My horse and saddle together are worth $132, and the horse is worth 10 times as much as the saddle: what is the value of the horse. Ans. $120.

44. Four persons traded together on a capital of $6000, of which A put in, B put in 1, C put in, and D the rest; at the end of 4 years they had gained $4728. what was each one's share of the gain?

A's $2364.

B's $1182.

Ans.

C's $788.

D's $ 394.

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