5. A pyramid, base a square 6 ft. on a side, altitude 4 ft., slant height 5 ft.

6. A cone, diameter of base 4 in., altitude 7 in.

7. A triangular prism, sides of base 4 in., 5 in., and 7 in., altitude 11 in.

8. A cube, 8 in. on a side.

9. How many gallons of water will a cylindrical cistern hold if its diameter is 8 ft. and depth 20 ft.? (See § 110.)

10. The volume of a cylinder is 500 cu. in., and its base has a diameter of 10 in. What is its height?

11. The volume of a prism is 320 cu. ft., and its base is a square, 4 ft. on a side. Find the altitude.

12. A cylinder 25 ft. high has a capacity of 1000 cu. ft. What is the diameter of its base?

13. How many cubic yards of dirt will it take to make a fill 300 yd. long, 10 ft. high, and 30 ft. wide?

14. What must be the diameter of a cylindrical gallon measure 7 in. high?

15. A has a cylindrical cistern, diameter 4', depth 10'. What is the diameter of B's cistern of the same shape and depth, holding 8 times as much as A's?

16. The volume of a cube each edge of which is 6'' is how many times as great as that of a cube each edge of which is 2''?

17. How many square yards of tin will be required to make 42 cylindrical pails, without covers, 10" in diameter and 12" deep, allowing 4 sq. ft. for seams and waste on each dozen pails?

18. A rectangular swimming pool is 60 yd. long, 80 ft. wide, and 10 ft. deep. How long will it take to fill it with water to within 3 ft. of the top, if the water runs in at the rate of 8 cu. ft. per second?

PRACTICAL MEASUREMENTS

160. Papering is estimated by the roll, either single roll (18 ft. long by 18 in. wide), or by the double roll (48 ft. long by 18 in. wide). It is more economical to use double rolls on account of the saving in matching the pattern.

NOTE. Imported papers vary in length and width.

161. Use the following rules for estimating the number of rolls required for any given room:

1. Deduct the width of all openings (doors and windows) from the perimeter of the room. Divide this result by the width of the paper to determine the number of strips required for the walls. The length of each strip will be the height of the room.

2. Divide the width of the ceiling (width of the room) by the width of the paper to determine the number of strips required for the ceiling. Each strip will be the length of the room.

3. Determine the number of strips (of each kind) that can be cut from a roll, and divide this into the number of strips required to determine the number of rolls required.

NOTE. Spaces above and under doors and windows (not allowed for in the above calculations) can usually be covered with the strips left over in matching the pattern.

162. Painting and plastering are estimated by the square yard. Make allowance for openings, unless otherwise directed. NOTE. Contracts usually specify allowances for openings.

163. Carpet is sold by the linear (running) yard; linoleum by the square yard.

PAPERING, PAINTING, PLASTERING

101

Carpets vary in width; this, as well as the matching of the pattern, must be taken into account in figuring the number of yards necessary for a given floor. The strips are laid the long way of the room.

EXERCISES

1. Find the cost of plastering, papering, and carpeting a room 20 ft. long, 16 ft. wide, and 10 ft. high (20′ × 16′ × 10′). It has 5 windows, each 6' x 3', 2 doors 7' x 3', and 1 door 7' x 6'. Paper costs $1.12 per double roll; plastering costs 40 per square yard; the carpet is yd. wide, at $2 per yard. PLASTERING

866 × $.40 = $38.49, cost at 40 per square yard.

9

45'18" (3) 30 strips, each 10' long, for the walls.

16' 3' 10 or 11 strips, each 20' long, for the ceiling. ÷

=

As each roll is 48' long, 4 ten-foot strips or 2 twenty-foot strips can be cut from each roll.

Hence, 3047, or 8 rolls for the walls.

11÷2=5, or 6 rolls for the ceiling.

Total required is 8 +6 or 14 rolls.

14 × $1.121 = $ 15.75.

CARPETING

As the room is 16' wide, as many strips of carpet will be required as yd. (the width of the carpet) is contained in 16'. 16 ÷ 2 = 71, or 8 strips, each 20' long.

₫ yd. = 21'.

2. At 20 per square yard, how much will it cost to plaster the walls and ceiling of a room 18' x 15' x 7'4", making allowance for 2 doors 7' 6'' x 3' 6", and 3 windows 61 × 3′ ?

3. A room is 15' x 12' x 9'. How much will it cost to paper it at 371 per double roll, allowing for 2 doors 8' x 4' and for 2 windows 6' 4' x 3' 3''?

4. A wall is 16' long and 12' high. How many double rolls of paper will it take to paper it, no allowance being made for openings?

5. A barn is 100' x 60' x 30', with gables 20' above the walls. If no allowance is made for openings, what will it cost to paint it at 5 per square yard?

100'

60'

6. How many yards of carpet 1 yd. wide will it take to cover a room 14' x 10', strips running lengthwise?

7. How many yards of carpet yd. wide will it take to cover the library, dining room, and living room, in the

accompanying floor plan, no allowance being made for matching patterns?

8. How many yards of linoleum will it take to cover the kitchen?

9. How much will the carpet in problem 7 cost at $1.33 per yard?

164. Roofing and flooring are usually measured by the square of 100 square feet. Flooring is sometimes measured by the 1000 board feet.

165. The most common roofing materials are: slate, tiling, shingles, and tin.

The size of slate used is generally 12" × 6", or 24′′ × 16′′.

NOTE. Contractors use a table for estimating the amount of slate to be used.

The size of shingles used is generally 16" x 4", or 18′′ × 4′′. 16" x 4" shingles are laid with 4" exposed to the weather.