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WRITTEN EXERCISES.

1. What is the area of a triangle whose base is 35 inches and altitude 20 inches?

2. How many square yards in a triangular garden whose base is 45 ft. and whose altitude is 32 ft.?

3. How many acres in a triangular field whose base is 20 chains and altitude 15 chains?

4. A triangular field contains 16 A.; what is its altitude if it is 160 rods long?

5. What is the base of a triangular field whose altitude is 18 feet and whose area is 60 sq. yd.?

6. Find the area of a triangle whose base is 560 rods and altitude 90 chains.

7. Find the area in square feet of a triangle whose base is 16 feet and altitude 5 feet.

8. Find the area in square yards of a triangle whose base is 8 yards and altitude 6 feet.

9. What part of an acre is a triangle whose base is 821 feet and altitude 2 chains

THE CIRCLE.

142. A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the centre.

The Circumference is the bounding line; as, A DBE. Any part of the circumference, as BD, EF, etc., is an Arc. The Diameter is a straight line passing through the centre and terminating in the circumference; as, A B, DE. The Radius is a line drawn from the centre to the circumference; as, CD, C F, etc.

RULE.

I. To find the circumference of a circle, multiply the diameter by 3.1416.

II. To find the diameter of a circle, divide the circumference by 3.1416 or multiply the circumference by .3183.

III. To find the area of a circle, multiply the circumference by one-fourth of the diameter, or multiply the square of the radius by 3.1416.

To square a number, multiply it by itself.

WRITTEN EXERCISES.

Find the circumference of a circle whose―

1. Diameter is 10 inches.

2. Radius is 10 inches.

3. Diameter is 31 feet.
4. Radius is 50 rods.

Find the diameter of a circle whose

5. Circumference is 10 feet.
6. Circumference is 40 inches.
Find the area of a circle whose-

9. Radius is 10 inches.
10. Diameter is 40 feet.
13. The diameter of a circular
its area?

7. Circumference is 80 rods.
8. Circumference is 200 chains.

11. Circumference is 100 rd. 12. Radius is 18 feet.

fish-pond is 40 feet; what is

14. Find the circumference of a circular window whose diameter is 3 feet.

15. A horse is tied to a stake by a rope 22 feet long; over how much space can he graze?

16. A pond 20 rods in diameter has a walk around it 6 feet wide; what is the area of the walk?

17 What is the area of a circle whose radius is a mile?

18. The area of a circle is 1 A. 154.16 P.; what is its circumference?

19. A wagon-wheel is 3 ft. 6 in. in diameter; how many miles does it travel in revolving 5000 times?

PAINTING, PAPERING, PLASTERING, ETC.

143. Painting, papering, plastering, etc. are estimated by the square foot or square yard.

Roofing is generally estimated by the square, which consists of 100 square feet.

Shingles are estimated by the thousand. With shingles that average 4 inches in width and are laid

6 in. to the weather, 600 shingles cover a square.

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WRITTEN EXERCISES.

1. What will it cost to paint a house 40 feet long, 30 feet wide, and 20 feet high, at 15 cents a square yard, no allowance being made for doors or windows?

2. What will it cost to plaster 6 rooms, each 20 ft. long, 15 ft. wide, and 10 ft. high, at 40 cents a square yard?

3. What will it cost to slate a roof 40 ft. 6 in. long, each side being 24 ft. wide, at $16 a square?

4. A roof is covered with shingles put 8 in. to the weather; what is the cost at $12 a thousand if the roof is 80 ft. long and each side is 30 ft. wide?

5. What will it cost to paint a barn 30 ft. long and 20 ft. wide, 16 ft. to the eaves, the gables being 8 ft. high, at 40 cents a square, if it requires 10 gallons of paint at $1.60 a gallon?

6. What will it cost to cover a room 24 feet long and 18 feet wide with carpet 27 in. wide at $1.25 a yard, allowing 5 yards for matching; the strips to be laid lengthwise?

7. What will it cost to cover a hall 33 feet long and 5 feet wide with matting 30 inches wide at 55 cents a yard?

8. What will it cost to cover the roof of a barn 80 feet long and 56 feet wide with shingles which average 4 inches in width and are put 8 inches to the weather, the length of the rafters being of the width of the barn, and the shingles costing $12 per thousand?

9. What will it cost to cover a floor 18 ft. long and 12 ft. 3 in. wide with oil-cloth at 50 cents a square yard?

10. Which will be the cheaper, and how much, to cover a floor 25 feet long and 22 ft. 8 in. wide with matting in strips 2 ft. 10 in. wide, laid lengthwise, at 45 cents a yard, or to cover it with oil-cloth at 50 cents a square yard?

11. What will it cost to plaster a room 18 ft. long, 12 ft. wide, and 10 ft. high, at 41 cents a square yard, allowing 90 sq. ft. for doors and windows?

12. How many rolls of paper, each containing 36 sq. ft., will be required to paper a room 16 ft. long, 15 ft. wide, and 10 ft. high, no allowance being made for doors and windows?

13. What will the paper cost for a room 20 ft. long, 16 ft. wide, and 12 ft. high, with paper 18 in. wide and 8 yd. long, at 20 cents a roll, allowing 100 sq. ft. for doors and windows?

14. What will it cost to paper a room 21 ft. long, 15 ft. wide, and 10 ft. high, with paper 18 in. wide and 8 yd. long, at 24 cents a roll, allowing for 3 windows 6 ft. by 3 ft., and 4 doors 7 ft. by 34 ft., if the work can be done by 2 men in 1 day at $2.50 each per day?

15. A frame barn is covered with shingles put 6 in. to the weather; what is the cost at $11 a thousand if the roof is 60 ft. long, each side being 32 ft., the first course along the eaves being doubled?

16. How many yards of plain matting 30 inches wide will be required to cover a hall 65 feet long and 30 feet wide, there being no allowance for waste and the strips running lengthwise? How many yards if the strips run crosswise?

MEASURES OF VOLUME.

144. A Volume is that which has length, breadth, and thickness. A volume is called a solid.

THE RECTANGULAR SOLID.

A Rectangular solid is a volume bounded by six rectangular faces.

A Cube is a volume bounded by six equal squares.

The Contents of a volume is the number of cubic units it contains. Thus, in the volume ABCDEF the contents is the number of small cubes it contains, which is equal to the number in the base multiplied by the number of layers; hence the whole number of cubes, or the con

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tents, equals the product of the length, breadth, and thickness. Hence the

RULE.

To find the contents of a rectangular volume, take the product of the length, breadth, and height.

WRITTEN EXERCISES.

1. How many cubic feet in a rectangular block 8 ft. long, 6 ft. wide, and 4 ft. high?

2. How many cubic yards of earth in a cellar 36 ft. long, 24 ft. wide, and 5 ft. deep?

3. Find the contents of a cube 8 ft. 6 in. on a side.

4. How many cubic feet of water in a rectangular reservoir

What is its weight,

80 ft. long, 60 ft. wide, and 10 ft. deep? if a cubic foot of water weighs 62 lbs.?

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