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MAA40S - Mr. S. Koslowsky
MAA40S - Mr. S. Koslowsky
Design & Measurement
The overall goal of this unit is for you to develop critical thinking skills related to
measurement and design. Since the curriculum for this section is fairly broad and open
ended, we will not spend a lot of time covering new material in class. Rather, you will
have to draw on your previous experience involving length, surface area, volume, unit
conversions, costs, taxes and design ideas in general.
If you're interested, here's a look at the specific learning outcomes in the curriculum:
.
.
Solve a problem involving perimeter, area, and volume using dimensions and unit prices.
Solve a problem involving estimation and costing for objects, shapes, or processes when
a design is given.
. Identify and correct errors in a solution to a problem that involves costing for objects,
shapes,or processes.
Estimate the solutions to complex measurement problems using simplified models
. Design an object, shape, layout, or process within a specified budget.
This booklet is a compilation of the design and measurement questions that have
appeared on the provincial exams for the last 3 years. Your goal is to work through
these problems, building your confidence with dealing with these types of situations.
This unit can be very useful in real life if you have any intentions of design or building
anything in the future.
You may work independently on these questions or work together. Just make sure that
you are building your skills in this area since you have to write your exam
independently.
You'll find some formula sheets at the end, but you may have to look up additional
equations. The formula sheet on your final exam should include what is needed to
answer the particular questions that were chosen.
Good luck!
DESIGN AND MEASUREMENT
Question No. 21
Total: 2 marks
133
The Bertrands want to empty their circular swimming pool. There is 3 feet of water left in the
pool which has a diameter of 16 feet. Using a pump which can remove 400 ft of water per hour,
how many hours will it take to remove all the water?
Applied Mathematics: Student Booklet (January 2013)
29
Question No. 22
Total: 4 marks
You have been asked to install floor tiles and paint your aunt's bathroom based on the following
information:
. The floor measures 5 ft. x 7ft.
. The walls are 8 ft. high.
. The door measures 80 in. x 30 in.
. The window measures 24 in. x 30 in.
a) You must cover the entire bathroom floor with tiles. Each tile measures 1 ft. x 1 ft. You
will need an extra 5% of tiles to account for waste. How many tiles will you need to
purchase for the project?
(1 mark)
30
Applied Mathematics: Student Booklet (January 2013)
134
135
b) You must apply two coats of paint to the walls of the bathroom. The door and the window
will not be painted. Determine the total area to be painted. How many cans of paint will you
need to purchase if one can covers 100 ft2? Show your work.
(3 marks)
Applied Mathematics: Student Booklet (January 2013)
31
DESIGN AND MEASUREMENT
Question No. 18
Total: 2 marks
A cake mix will produce 230 cubic inches of batter. You are using cylinder-shaped baking cups
that have a diameter of 3 inches and a depth of 2 inches for the batter. How many cupcakes will
you be able to make? Show your work.
28
Applied Mathematics: Student Booklet (June 2013)
130
Question No. 19
Total: 2 marks
131
A goat is tied to the comer of a barn with a 50-foot rope. The barn measures 60 feet by 40 feet.
Calculate the total area outside of the barn that is available to the goat. Show your work.
40ft.
60ft.
Applied Mathematics: Student Booklet (June 2013)
29
Question No. 20
Total: 4 marks
132
The Manitoba Beach Volleyball Association has asked you to design a souvenir beach ball
according to the following information:
. The beach ball must have a volume between 1 and 3 cubic feet.
. The plastic material costs $0.15 per ft .
. Labour and other materials cost $ 1.25 per beach ball.
. The Association wants to make a profit of 80% of the cost of making each beach ball.
Based on your design, what is the minimum selling price for each souvenir beach ball? Show
your work.
30
Applied Mathematics: Student Booklet (June 2013)
DESIGN AND MEASUREMENT
Question 22
Total: 1 mark
What is the minimum amount of paper required to create the cone-shaped paper cup shown
below? (Diagram is not drawn to scale.)
5 cm
Select the correct answer.
A) 37.70cm2
B) 47.12 cm2
C) 75.40 cm2
D) 113.10cm2
28
Applied Mathematics: Student Booklet (January 2014)
134
Question 23
Total: 2 marks
135
A student was given the following diagram and was asked: "How many cubic yards of soil are
required to fill this garden with 4 inches of soil?" (Diagram is not drawn to scale.)
4 in.
9ft.
18ft.
The student provided this answer: 18 x9 x-= 54ft3 = 18 yd3
Explain the student's error and provide the correct answer.
Applied Mathematics: Student Booklet (January 2014)
29
Question 24
Total: 3 marks
A bathroom floor is covered by 15 floor tiles. Each tile measures 18 in. X 18 in.
136
a) How many floor tiles measuring 6 in. X 6 in. would be needed to cover the same area?
Show your work.
(2 marks)
b) You would like to redo the floor with 6 in. X 6 in. tiles. These tiles are sold in packages of
5 tiles and cost $4.00 per package (taxes included). How much would it cost to buy the
nximber of tiles you calculated in (a)?
(1 mark)
30
Applied Mathematics: Student Booklet (January 2014)
137
DESIGN AND MEASUREMENT
Question 21
Total: 2 marks
132
Philippa wants to cover her dining room floor with linoleum. The floor measures 14 ft. xl2 ft.
The linoleum costs $13.99 per square yard and must be purchased in whole units.
What will be the total cost for the flooring, including taxes? Show your work.
(Note: GST = 5%, PST = 8%)
30
Applied Mathematics: Student Booklet (June 2014)
Question 22
Total: 4 marks
133
Mackenzie Construction was awarded the contract to build gravel shoulders along the highway
between Wabowden and Thompson. (Diagram is not drawn to scale.)
The gravel shoulders will be
gravel shoulders
. along a 22 mile segment of the highway
. on both sides of the highway
. 10 feet wide
. 20 inches deep
Note: 1 mile = 5280 feet
20 in.
How many truckloads of gravel will be needed for the project if a truck holds 20 cubic yards of
gravel? Show your work.
Applied Mathematics: Student Booklet (June 2014)
31
DESIGN AND MEASUREMENT
Question 20
Total: 5 marks
The zoo has asked you to design a structure for its monkeys and owls using the following
guidelines:
. The structure will back against the wall of a building and will be fenced at the top, front, and
sides. (No fence is needed on the ground or at the back.)
. The structure will be divided into two enclosures by a separation fence and have a height
of 15 ft.
. The monkeys require an enclosure with a ground area between 600 fit and 1 000 ft2.
. The owls require an enclosure with a ground area between 400 ft and 800 fit2.
. The entire structure will be created using chain-linked fence, which is sold in 50 ft. x 5 ft.
(250 ft2) segments. Each segment costs $160.00, plus GST and PST.
Buildmg Wall
Monkey Enclosiue
Top
Owl Enclosure
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132
a) Determine a possible set of dimensions for your design.
(1 mark)
Ground dimensions of monkey enclosure:
Ground dimensions of owl enclosure:
24
ft. x
ft. x
ft.
ft.
Applied Mathematics: Student Booklet (January 2015)
133
b) Determine the minimum number of fence segments needed for your design. Show your
work.
(3 marks)
134
c) Calculate the total cost of the structure. (Note: GST = 5%, PST = 8%)
(1 mark)
Applied Mathematics: Student Booklet (January 2015)
25
Question 21
Total: 2 marks
135
The coffee mug shaded in the diagram below is based on a cone with the bottom portion
removed. (Diagram is not drawn to scale.)
12cm
12cm
Determine the volume of the mug. Show your work.
26
Applied Mathematics: Student Booklet (January 2015)
DESIGN AND MEASUREMENT
Question 22
Total: 1 mark
Select the best answer.
133
How many cubic yards are in 54 cubic feet?
A. 2
B. 3
C. 6
D. 18
Question 23
Total: 1 mark
34
One can of paint can cover an area of 200 ft .
How many cans need to be purchased to paint a 60 ft. by 8 ft. wall?
Applied Mathematics: Student Booklet (June 2015)
25
Question 24
Total: 5 marfcs
James is landscaping his 50 ft. by 40 ft. yard. He will construct a concrete walkway with a
uniform width of x around the centre of the yard which is to be covered in sod, as illustrated
below. (Diagram is not drawn to scale.)
Consider the following:
. The walkway must be at least 3.5 feet wide.
. The concrete must be poured 6 inches deep.
. The concrete costs $3.00 per cubic foot, plus GST and PST
. The sod costs $0.40 per square foot, plus GST and PST.
. The budget for this project is $2150.00.
a) Design a walkway that fits within the budget. Indicate the width of the walkway and the
dimensions of the sod below.
(1 mark)
Width of the walkway (x):
Dimensions of the sod:
26
ft.
.ft. by
ft.
Applied Mathematics: Student Booklet (June 2015)
135
136
b) Calculate the total cost of your design. (Note: GST = 5%, PST = 8%)
(4 marks)
Applied Mathematics: Student Booklet (June 2015)
27
MAA40S - Mr. S. Koslowsky
Conclusion
Please reflect on your learning process as you worked through these problems.
What did you learn about your personal skills and interests from doing the problems in
this unit?
What types of activities or workplaces would require the use of design and
measurement skills?
Describe situations or activities that would give you an opportunity to apply what you
have learned in the Design and Measurement unit.
Senior 4 Applied Mathematics (40S)
Design and Measurement
Portfolio
Formulas
Area
Perimeter
(in square uaaits)
(in luuta of length)
square
A = a2
p =4a
rectangle
A=a6
Figure
Diagram
p = 2(a + b)
or
p=2a+26
a ^
A = aft
parallelograin
/T~\
j» =2a + 2&
A=^(a+b)h
p=a+&+c+d
triangle
A=^h
p =a +6 + c
circle
A=?rr2
C=2jtr
trapezoid
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Senior 4 Applied Mathtmatics (40S)
Desi^i and Measurement
POTtfoUo
Figure
Diagram
Surface Area
(in square unita)
0:
rectangular
solid
u>
SA = 4jrr2
sphere
SA =ws
cone
cylinder
SA=
2wh^2lw+2lh
(slanted side only)
Volunae
(in cubic iinits)
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. V^lwh
v-t"'
V.yr'l,
n
.t
SA s 2m-h + 2a^
SA=2sb
pyramid
(all four sides not the bottom)
V=^A
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0
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