Socrative Carpenters Math Flashcards
- Determine the number of square feet of exterior wall area in the
building illustrated to the right, given a 14’ 0” wall height
2,380 ft²
- Determine the run of each step as indicated by Dimension B in
the illustration.
10”
Take your total un and divide it by the number of units of un:
10inches
/tread
B = 40” ÷ 4 units of un =
20.Given the information on the right, what is the elevation at point
B?
Elevation = Height of instument - foresight reading
= 107.55’ - 4.93 = 102.62’
- Both side of the roof shown on the right are covered with asphalt
shingles. What is the the area to be covered?
1,338.75 ft²
Convert your width and length into decimal feet, and multiply one by the other to get your roof area for
one side and then double it to take the other side into account:
width = 15’9” = 15.75’
length = 42’6” = 42.5’
total area = (15.75’ X 42.5’) X 2 = 1,338.75 ft²
30.What is the floor area of the semicircular bay window pictured on
the right?
19.24 ft²
Because it is a semi circle, you can just calculate the area for a whole circle with the given radius and
then divide it by 2:
use pi = 3.1416
- What is the capacity of the silo on the right (from top of slab to top of
walls) ?
10,730.13 ft³
36.How many cubic yards of concrete would be required for the walls of
the silo on the right?
First, calculate the center line circumference of the silo walls to determine your length in linear feet:
use p= 3.1416
center line diameter = inside diameter + 1 wall thickness = 18’ + 0.5’ = 18.5’
center line circumference= center line diameter X p = 18.5’ X 3.1416 = 58.1196’
Next, multiply your center line circumference by the thickness and height of your wall to get your volume
in cubic feet, and then divide it by 27 to convent it into cubic yards:
center line circumference = 58.1196’
wall thickness = 6” = 0.5’
height = 42’6” = 42.5’
27f
t³/yd.
volume = 58.1196 X 0.5’ X 42.5’
= 1,235.0415 ft³ ÷27
= 45.742 yd³ ˜ 45.74 yd³
37.A shed roof measuring 16’ X 28’ is covered with asphalt shingles. If the shingles weigh 235 lbs.
per square, and the nails weigh 4.5 lbs. per square, what is the total weight of the shingle and
nails you installed?
1,072.96 lbs.
First, calculate the total area of your roof in square feet and divide your total by 100 (1 square of shingles = 100 ft²):100ft²/square =roof area = 16' X 28' = 448 ft² ÷4.48 squares
Next, multiply the weight per square of your shingles by the number of squares, multiply the weight per square of your nails by the number of squares, and add your two weights to get your total material weight: 235lbs/ square weight of shingles = X 4.48 squares = 1,052.8 lbs. 4.5lbs /square weight of nails = X 4.48 squares = 20.16 lbs. total material weight = 1,052.8 lbs. + 20.16 lbs. = 1,072.96 lbs.
46.How much concrete can be placed into a cylindrical form with a diameter of
28” and a height of 35 7.5”?
5.6 yd³
First, convent your dimensions into decimal feet: inches/foot diameter = 28" ÷ 12 inches/foot = 2.33334 ' height = (7.5" ÷ 12+ 35' = 0.625' + 35' = 35.625' Next, use your diameter to determine the circular area of the top of your form:
use pi = 3.1416 radius (r) = diameter ÷ 2 = 2.33334' ÷ 2 = 1.16667' area of circle = p² = (3.1416)(1.16667')² = 4.2760911 ft²
Next, multiply your area by your height to calculate your volume in cubic feet:
volume = area of circle X height = 4.2760911 ft² X 35.625’ = 152.335745 ft³
Finally, divide your cubic feet by 27 to convert your volume into cubic yards:
ft³/yd³
152.335745 ft³ ÷ 27
= 5.64206 yd³ ˜ 5.6 yd³
47.Three skids of lumber are ordered:
1 @ 10’ long X 8’ wide X 6’
high,
1 @ 14’ long X 8’ wide X 8’ high, and
1@ 16’ long X 8’ wide X
10’ high.
How many board feet of lumber is this?
31,872 BF
i The formula for board feet is: BF = height(in inches) X Width(in inches) X length(in feet) 12 First, convent your heights and widths into inches, keeping your skids separate: Skid 1 12inches/foot= height = 6' X 72" 12inches/foot= width = 8' X 96" length = 10' Skid 2 12inches/foot= height = 8' X 96" 12inches/foot= width = 8' X 96" length = 14' Skid 3 12inches/foot= height = 10' X 120" 12inches/foot= width = 8' X 96" length = 16' Next, plug your dimensions into the board foot formula to get each skid's volume, and then add your quantities to get your total: Skid 1 BF = height(in inches) X Width(in inches) X length(in feet) 12 = 72" X 96" X 10' = 5,760 BF 12 Skid 2 BF = height(in inches) X Width(in inches) X length(in feet) 12 =96" X 96" X 14' = 10,752 BF 12
Skid 3
BF = height(in inches) X Width(in inches) X length(in feet)
12
=120” X 96” X 16’ = 15,360 BF
12
Total volume = 5,760 BF + 10,752 BF + 15,360 BF = 31,872 BF
48.An ellipse has a major axis of 175mm and a minor axis of 68mm.
To replicate the same ellipse at a larger scale with a minor axis of
300m, what size will the major axis be?
772 M
convent all measurements into meters: Original ellipse: 1,000mm/M= major axis = 175 mm ÷ 0.175 m 1,000mm/M= minor axis = 68mm ÷ 0.068 m New large scale ellipse: major axis = x minor axis = 300 m Next, solve for x using ratio and propotion: 300m x . = 0.175m 0.068m . =.
= 772.0588m˜772m
x
51. 0.0579inches/hour. You are using constuction grout that cures at at rate of How long will it take 95/8" for a section that is deep to cure?
1 week
First, convert the thickness into decimal inches: 5 ÷ 8 = 0.625" + 9" = 9.625" Next, divide the thickness by the rate of cuing to get your answer in hours: 0.0579inches/hour= 9.625" ÷ 166.2348877 hours ˜ 166.235 hours Finally, divide your hours by 24 to convert into days: 166.235hours ÷ 24hours/ day 6.9264583days ÷ = ˜ 7days = 1 week
- What is the length of the sides of an octagon whose overall width is
12’ -8”?
The easiest way to calculate the length of the sides of an octagon is to draw a
square with four sides measuing the desired width of your stucture,
calculating the hypotenuse and subtract the dimension of one side from the
hypotenuse dimension. The remainder will represent the length of each side:
Hypotenuse =
Length of sides = hypotenuse - desired width
= 17.9133765’ - 12.66667’
215/16”
= 5.2467065’ ˜ 5’
- A 45° bay window is laid out as shown. What is the dimension of
the long side of the bay?
Because it is a 45° bay window, the lateral dimension of the sloped windows will be the same as their
31/2”).
projection from the building 2’
Therefore, to calculate the length of the long side, multiply the
projection by two to account for both sides, and deduct it from the overall measurement:
31/2”
2 X 2’
= 4’7”
length of long side = 11’10” - 4’7” = 7’3”
- What is the area of the triangle on the right?
13,717.456 ft²
First, convert your measurements into decimal feet: 12inches/foot= Base: 14 = 0.25" + 11" = 11.25" ÷ 0.9375' + 219' = 219.9375' 12inches/foot= Height: 7 ÷ 8 = 0.875" + 8" = 8.875" ÷ 0.739583' + 124' = 124.739583' Next, enter your values into the corresponding formula: height Area of a triangle =×base2 = 219.9375' X ² t² = 13, 717.4565018f t² ˜13, 717.456ft
- Given the following roof specifications, what is the slope of the roof?
South end elevation= 275.305’
North end elevation= 269.488’
End to end distance= 185’
3.14%
slope of roof = south end elevation - north end elevation X 100
End to end distance
- A builders’ level reads a back sight of 3.011’ over a known
elevation point of 785.232’. What is the height of instrument?
788.243’
A builders’ level reads a back sight of 3.011’ over a known
elevation point of 785.232’. What is the height of instrument?
Height of instrument = known elevation + back sight = 785.232’ + 3.011’ = 788.243’
What is the area of the triangle on the right?
Question #58
130,625 mm²
What is the area of the triangle on the right?
Area of a triangle = base x height/2 = 950 mm x 275 mm /2 = 130,625 mm squared
- Find the cost of 28 squares of asphalt shingles at $37.00 per square.
1,036
- If it takes 19 board feet, including waste, to build a table then how many board feet would you
need to build 54 such tables?
1,026
- How many square feet of floor area does the building from
question 3 contain?
1,237 square foot
5.One carpenter can apply 24 ft² of siding per hour. At the same
rate, how long does it take a crew of 6 to put on 11, 952 ft²
of siding?
83 hours
6.How many joists would you need to frame a 52’ long floor at 16” on centre?
40
7.The illustration shows a shot flight of steps, where dimension A
is the
height or rise of each step. Determine dimension A.
7”
9.The specifications for a building state that the spacing for floor joists is 2’ on centre. How many
floor joists would you need to frame a floor that is 116’ long?
59
- Shingles are laid so that 4 3/4”
are exposed in each course. What linear distance would be
covered up the roof if 28 courses were applied?
11’ - 1 “
- What width of board is required for the stair treads shown in the
illustration on the right?
10 7/8”
- What is the horizontal distance B in the illustration on the ight?
40”
13.If a drawing is scaled at 1/4” : 1’0”, how long would a line need to be to represent 18’0”?
4 1/2”
- When 1”X8” bevel siding is applied to a building with 6 3/4” exposed to the weather, what height
would be covered by 15 courses?
101 1/4”
- The material needed for a deck is estimated to be 81.9 BF. What would the total cost of material be at a price of 1.65$/BF?
$135.14
- If a stack of 3/8” plywood is 20 1/4”
tall, how many sheets high would it be?
54
- In setting form work for a sidewalk, a carpenter is asked to raise the form 3/4” above an
elevation of 141.35’. What is the new elevation?
141.4125’
- Given the information on the right, what is the height of the
instrument?
107.55’
19.Given the information on the right, what is the elevation at point
A?
100.20’
- If an excavation cost of $674 represents 2% of the total cost of a project, what is the total cost
of that project?
$33, 700
- If the $1,800.00 you make on a job represents a 12% profit, what was the total cost of the job
for your client?
$15,000.00
- A dining room floor measures 12’0” wide and 12’6” long. At a rate
of 60 cents per square foot, how much would it cost to sand this
floor
$90.00
- How many square feet of surface does the roof from question 25 contain if the ridge length is
changed to 33’9” long?
1,063.125 ft²
- How much would it cost you before tax to purchase 32 panels @ 4’0” X 8’0” if they cost
$0.30 per ft²?
$307.20
- What is the area of the hip roof shown on the ight with four sides
at 22’0” long and a total rafter length of 14’6” including
projection?
638 ft²
- What is the area of the formwork on the end of the retaining wall on
the ight?
- 3125 ft²
- A rough floor is laid under the space occupied by the gymnasium
track shown on the ight. Determine the area occupied by the
track. Do not include the space inside the track
899.78 ft²
- How many cubic yards of concrete are needed to pour eight footings @ 20” X 20 “ X 8”
0.549 yd³
- How many cubic yards of concrete would you need to remove to
create the excavation on the ight if it was 8’0” deep?
3,792.59 yd³
34.
How many cubic yards of concrete would you need to fill a form
that is 2’ wide, 7’ high and 684’ long?
354.667 yd³
38.
What is the area of a circle with a radius of 10’?
314 ft²
39.
Using the illustration on the ight, If line AB= 45’0” and AD =
27’0, what is the total length of diagonals AC and BD?
52’ - 5 3/4”
40.
In checking to find out if the corner at point D is square, GD is laid
out at 9’0” and DH is laid out at 12’0”, what should the length
GH be?
15’ - 0”
41.
What are the lengths of diagonals AC and BD, if AB and BC are
each 41’ 6”?
58’ - 8 1/4”
42.
How many cubic feet of concrete is there in a form containing 750 cubic inches?
0.43 ft³
43.
Convert 1,095 yd³ into ft³
29,565 ft³
44.
What is the area of a circle with a 6,000 mm diameter?
28.3 m²
45.
What is the volume if the prism on the ight?
74.1 m³
49.
What is the length of RA on the right?
813.295
50.
What is the length of XZ on the right?
2,464.62
55.
What is the distance from point A to point B in the drawing on the
right?
149’ 1/8”
59.
What is the perimeter of the figure shown on the right?
219.93 m
60.
Top of steel at one end of a roof is 25’ 1 1/4” .If the roof has a 6% slope, what is the elevation at
the other end of the building if it it 52’ long?
28’ - 2 11/16”
21.
Given the information on the right, what is the difference
between point A and point B?
2.42’
