10. A log of wood is 15 inches broad and 11 inches thick. What length of it will make 10 cubic feet?

11. What rate per cent is required to make $10,050 gain $682.005 interest in 11 months and 19 days?

12. How long will it take $16,500 to gain $2,117.50, at 7 per cent?

13. A merchant imported 120 tons of English iron, costing 1 pence per pound, on which he paid a duty of 20 per cent. The freight was 5 shillings sterling per ton. What was the total cost in U. S. currency? (1 ton = 2,240 lb. £1 = $4.8665.)

14. Reduce the following complex fraction to its simplest form:

81)
8
X
16

15. Samuel Adams, a contractor, had the following dealings with the Treasury Department: He furnished, January 3, 1883, 2,575 lb. of twine at 12 a lb.; April 4, 1883, 25 doz. gold pens at $25 a doz.; May 7, 1883, 645 reams letter paper at $2 a ream; July 9, 1883, 45 doz. qt. Arnold's ink at $3 a doz.; October 30, 1883, 1,000,000 envelopes, at $2 a thousand; and December 5, 1883, 8 doz. inkstands at $1.97 a doz. He was paid cash as follows: February 4, 1883, $175; April 30, $350; July 15, $700; November 5, $2,300; and December 31, 1883, he was allowed on settlement $45 for cartage, and charged $75 for breakage, and $60 for shortage on envelopes. State his account in the blank below, with proper heading, and show the balance, if any, due him. (No interest.)

1123. Questions from Examinations for N. Y. State Certificates. 1. The large wheel of a bicycle is 15.7 feet in circumference. How many times must it revolve in running a mile?

2. How many rods of fence are required to enclose a square lot whose area is 5,184 sq. ft.?

3. Property worth $6,000 is insured for of its value, at of one per cent. What will be the loss, including premium, in case of total destruction by fire?

4. Required the cost of laying a pavement 5 rods long and 8 ft. 6 in. wide, at $1.40 per square yard.

5. The sum of two numbers is 12 bu. 1 pk. 3 qt., and their difference is 1 bu. 2 pk. 5 qt. What are the numbers?

6. Make and solve a problem illustrating how the principal is found when the interest, rate per annum, and time are known, using 1 yr. 1 mo. 1 da. as the time.

7. Make and solve a problem illustrating the application of square root in finding the side of a right-angled triangle.

8. How many acres of land, in the form of a square, may be enclosed by 160 rods of fence?

9. Find the square root of .441 correct to two decimal places. 10. Reduce 17 lb. 11 oz. avoirdupois weight to pounds, ounces, pennyweights, and grains, troy weight. (1 lb. avoirdupois 7,000 troy grains.)

=

11. A note for $324.61, and interest, amounted to $384.13, 2 yr. 7 mo. 13 da. after date, when it was paid. Required the rate per cent per annum.

12. The premium on a fire insurance policy, at 7 of 1 cent, was $140. Required the face of the policy.

per

13. What is the length (in rods) of the diagonal of a square. field containing 40 acres?

14. Reduce 1513 to its lowest terms.

15. Find the solid contents of a cube, the area of one face of which is 256 square feet.

16. What elements are required to find the per cent of gain or loss in a business transaction? Illustrate by an original problem.

17. A car contains 21,643 pounds of wheat. Find the value of the load at 92 per bushel. (1 bu. 60 lb.)

18. Find the area of a triangle whose base is 22 ft. 8 in., and altitude 19 ft. 9 in.

19. The list price of a certain stove is $38, and the retail dealer is allowed commercial discounts of 20 per cent, 5 per cent, and 3 per cent. What price does he pay for the stoves?

20. If 45 horses eat 1 tons of hay in 30 days, how many tons should last 84 horses 56 days?

21. If a ton of coal lasts a family 21 days, what will be the cost of coal used by it from Oct. 17, 1888, to April 25, 1889, exclusive of either day named, at $4.50 per ton?

22. A farmer sold 48.64 acres of his farm of 112 A. 96 sq. rd. What per cent of his farm had he left?

23. Find the cost of a pile of 4-foot wood, 27 ft. long and 6 ft. high, at $5.50 per cord.

24. Find the interest on $1, for 3 yr. 1 mo. 29 da., at 5 per cent per annum.

25. Four men hire a pasture field together. The first pastures 4 cows 18 weeks; the second, 5 cows 124 weeks; the third, 11 cows 6 weeks; the fourth, 9 cows 16 weeks. What part of the rent should each pay?

26. How many rods of fence will be required to enclose a field in the form of a right-angled triangle, whose area is 13 acres and whose base measures 48 rods?

MENSURATION OF PLANE SURFACES.

1124. Slate Exercises.

1. Find the circumference of a circle whose radius is x.

(Diameter 3.1416.)

2. Find the area of a circle whose radius is x.

3. Find the area of a circle whose diameter is x.

4. Find the area of a circle whose circumference is x.

5. What is the area of a circle whose diameter is 36 feet?

6. What is the radius of a circle whose area is 153.9384 sq. yd.?

7. What is the circumference of a circle whose area is 198.95 sq. rods?

8. Find the area of a square whose diagonal is x.

9. Find the area of a square whose diagonal is 150 rods.

10. Find the area of an isosceles triangle, its base being 56 meters, equal sides 100 meters.

11. Find the area of an equilateral triangle whose side is 12 feet.

12. Find the area of a triangle whose sides are 50 yd., 60 yd., 70 yd.

13. What is the area of a circle whose circumference is 10 feet?

40 rd.

25 rd.

20. Find the altitude, AB, of the following triangle, Fig. 7:

21. Find the diagonal (in rods) of the square whose area is 5

FIG. 5.

acres.

22. Find the area of a hexagon, composed of six equilateral triangles, each side being 6 inches. Fig. 8.

23. What is the area of the circle circumscribed about the

above hexagon, Fig. 9?

24. What is the area of the square inscribed in a circle whose diameter is 10 feet, Fig. 10?