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302. Find the area of a sector, the radius of which is 16 in. and the arc. 27°.

303. A regular hexagon is inscribed in a circle, the diameter of which is 9 ft. Find the area of the

hexagon.

NOTE. The side of the hexagon is equal to the radius of the circle. 304. Find the cost of plastering a room 25 ft. 6 in. long, 17 ft. 3 in. wide, and 10 ft. 8 in. high. The price

for the walls is 21 cts., and for the ceiling 32 cts.
a square yard.

305. A circular plot of ground contains of an acre.
What is its diameter?

306. Find the volume of a square pyramid, if each side of its base is 4 ft. 6 in., and its altitude is 12 ft.

307. A line 62 ft. long reaches from the top of a house 48

ft. high, to the bottom of a house on the opposite

side of the street. Find the width of the street.

308. Construct a triangle whose sides shall measure 51 in., 4 in., and 23⁄4 in. respectively, and find its area.

309. Find the surface of a sphere whose diameter is 3.5 ft. 310. Find the volume of a sphere whose diameter is 25 in. 311. If the volume of a sphere is 33510.4 cu. in., what is its diameter?

312. A square field, containing 27 acres, has a diagonal V path across it. Find the length of the path in yards.

313. Find the capacity of a round basket 20 in. in diameter and 28 in. deep.

314. Find the volume of a triangular prism whose length. is 8 ft. 6 in., and the three sides of the base 2 ft. 6 in., 2 ft., and 1 ft. 6 in. respectively.

315. The diameter of a spherical balloon is 25 ft. How many square yards of silk were required to make it, and how many cubic feet of gas will be required to fill it?

316. Find the weight of an ivory ball 2 in. in diameter, the weight of ivory being 1825 oz. a cubic ft.

317. How many cubic feet in a stone roller 6 ft. 6 in. long and 5 ft. 4 in. in circumference?

318. The circumference of the base of a cone is 33 ft., and its height is 35 ft. Find its volume.

319. How many rolls of paper 12 yds. long and 22 in. wide must be bought to paper the walls of a room 27 ft. long, 201 ft. wide, and 11 ft. high?

320. The base of a pyramid is an equilateral triangle, each side of which is 8 ft., and the height of the pyramid is 13 ft. 6 in. Find its volume.

321. If a cylindrical tin canister, 3 in. in diameter and 63 in. in height, holds a pound of ground coffee, how much will a canister hold that is 4 in. in diameter and 8 in. in height?

322. If a pipe 2 in. in diameter discharges 20 gals. of water in a minute, how many gallons will be discharged in a quarter of an hour by a pipe 4 in. in diameter, the water flowing at the same uniform speed?

323. The horses employed to turn a threshing-machine move round at the distance of 15 ft. from the centre, and make 21 circuits in five minutes. At what rate per hour do they walk, reckoning π = 34 ?

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EXAMINATION PAPERS.

Paper 1.

1. Write in words the sum of 4,300,702, 6,070,506, and 341,318.

2. Divide 19,094,867 by 4009.

3. Express in words and in figures the excess of the value of one 5 over the other in the number 658,457.

4. Multiply seventeen thousand nine hundred forty-three by five thousand seventy-nine.

5. Find the number which subtracted from 80,000 leaves 57,735.

6. Divide five hundred one millions five hundred by three thousand eight hundred fifty.

Paper 2.

1. Add together 0.0023, 2.36, 250, 0.527.

2. Subtract 2.03 from 20.2.

3. Multiply 3.26 by 1.02.

4. Divide 998.824392 by 0.018.

5. Divide 1.8 by 500.

6. Divide 101 by 1.01; and 0.101 by 10.1.

Paper 3.

1. Find the G. C. M. of 203 and 2291.

2. Find the L. C. M. of 12, 21, 28, 30, 35.

3. Find the G. C. M. and L. C. M. of 144, 176, 272. 4. Find the L. C. M. of 8, 10, 12, 25, 30, 36.

5. Find the G. C. M. and L. C. M. of 161, 253, 299. 6. The imperial gallon of Great Britain contains 277.274 cu. in. What is the size of a pint pot in cubic inches? What weight of water will it hold, if a cubic foot of water weighs 1000 oz.?

Paper 4.

1. What number added to the sum of 3, 4, 4, and § will make 4?

2. A field of 3 acres is divided into 28 equal parts. What fraction of an acre is there in each part?

9

5

3. Find the product of 14, 27, 94, and 24.

4. Subtract 3 from 307.

5. Add †, 24, and 13; divide this sum by 13; and subtract the result from 5.

6. Add of a score to of a dozen, and subtract from the result of a hundred. What is the remainder?

7. The upper floor of a house is 18 ft. 4 in. above the ground and is reached by two equal staircases, separated by the landing of the first floor. How many stairs are there in each staircase, if each stair is 11 in. high?

Paper 5.

1. Reduce 125 sq. rds. 23 sq. yds. 6 sq. ft. 108 sq. in. to square yards.

2. How many grains in a pound Avoirdupois? in a pound Troy?

3. The latitude of St. Paul's in London is 51° 30'49", and that of St. Peter's in Rome 41° 53' 54". What

is one-fifth of the difference of their latitudes?

4. Reduce 3 qts. 1 pt. to the decimal of a gallon.

5. A dozen persons hire an omnibus for $9.25.

How

much more must each pay than if the party were
fifteen in number?

6. Find the G. C. M. of 3575 and 4719.

7. Express as a fraction of $5 the difference between $7 and of $7.

Paper 6.

1. Reduce 5 oz. 12 dwt. 16 grs. to the decimal of a pound. V 2. Divide of by of.

14694+

3. Express 0.0075 as a common fraction in its lowest

terms.

4. Find the value of 0.009943 of a mile in rods, etc.

5. A can do a piece of work in 10 dys. B can do the work in 15 dys. In what time can they both do it working together?

6. From 1 lb. Troy of standard gold are coined 46.725 sovereigns. Find the weight in grains of each sovereign.

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