Ohio State University Foundations of Mathematical Reasoning Algebra Questions

Please answer all 9 questions. Only take the question if you know what you are doing. Im uploading the assignment in word and in a pdf file. Its the same assignment.

Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
Practice Assignment 11.C
Questions 1 and 2: After doing some work in the house, Bob and Carol want to put a
concrete patio on the side of the house to keep people from tracking mud inside. The
dimensions of the rectangular patio are 23 feet 9 inches by 10 feet 1 inch. The patio will
need to be at least 2 inches deep.
1)
2)
Calculate the volume of concrete needed, in cubic yards, adding 5% to allow for
spillage and an uneven base, and round up to the nearest 1/4 cubic yard. Select
the best answer from the options below. a)
Order 3.25 yd3
b)
Order 1.75 yd3
c)
Order 3.75 yd3
d)
Order 11.25 yd3
Bob and Carol decide to hire someone to do the patio work. Rachel’s Ready-Mix
bid on the job is based on the information provided. The delivered cost of the
concrete is “$150 per yard (in increments of 1/4-yard) plus a $50 surcharge for
orders less than four yards.” (Concrete companies sometimes advertise “per yard”
when they really mean “per cubic yard.”) Find the total cost of the job to the
nearest cent (tax is already included in the charges and is not charged on the
delivery fee).
Questions 3–5: Recall Carol’s plans to plant 4 tree seedlings in the yard. She wants to
buy bark mulch to place in a circle with a 48-inch diameter around the base of each
tree. She has been told to lay the mulch 3 inches deep. The mulch is sold in bags
containing 2 cubic feet, for $4.49. Calculate the charge for the mulch, including 7.5%
sales tax.
3)
How many cubic feet of mulch does Carol need for the project? Round to the
nearest tenth of a cubic foot.
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
4)
What is the total charge Carol will have to pay to complete her mulch project?
5)
A local nursery is selling a scoop of mulch for $16 and charges $15 to deliver.
What is the total charge Carol will have to pay if she chooses to purchase the
mulch at the nursery instead?
6)
The volume of an object that is the same on the top and the bottom is typically
found by determining the area of the two-dimensional base figure and “stretching”
that base to the desired height. An example of this is the semicircle patio in
Question 1 from the in-class activity. Another example is shown below.
Box
Volume: 𝑉 = 𝐿 × 𝑊 × 𝐻 Variables:
𝑉 = volume; 𝐿 = length; 𝑊 = width; 𝐻 = height
In this case, the base figure is a rectangle (shaded) with
area = 𝐿 × 𝑊, which is multiplied by the height (𝐻) to get the volume of the figure.
Which of the following would be appropriate units of measurement for the different
parts of the figure?
7)
a)
Bottom edge (𝐿), the area of the bottom, and the volume are all measured in
inches.
b)
Bottom edge (𝐿) is measured in square inches; the area of the bottom is
measured in inches and the volume is measured in cubic inches.
c)
Bottom edge (𝐿) is measured in inches; the area of the bottom is measured in
square inches, and the volume is measured in cubic inches.
d)
Bottom edge (𝐿), the area of the bottom and the volume are all measured in
square inches.
The Ko family is going to clean up their yard after a storm. They go to a discount
store to purchase plastic containers for the clean-up. There are a variety of
containers with different shapes and sizes. Help the Ko family calculate the volume
of each container to the nearest cubic inch, assuming the round containers do not
taper.1
1
Sources: http://www.globalindustrial.com/g/office/garbage-recycling/containers-plastic/carlisle-bronco-roundwastecontainers-lids-95672, and http://www.globalindustrial.com/p/office/garbage-recycling/containers-plastic/35gallonsquare-rubbermaid-waste-receptacle-gray.
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
Containers
Size
Volume
1
19 inches
wide, 19
inches long and
27 inches high
1
19 inches wide, 19
and
inches long
2
1
34 inches high
4
Diameter of 24 inches and
31 inches high
Diameter of 29 4 inches
5
and 33 inches high
The following problems should be completed in your binder.
Questions 8–9: The formulas for finding the volume of three-dimensional geometric
figures that occur in everyday use are published in reference books or available online.
Use the web or some other source to find a formula for the volume of each figure.
Define each variable in the formula and label the figure with the variables to indicate the
correct meaning of the variable.
For example:
Box
Volume: 𝑉 = 𝐿 × 𝑊 × 𝐻 Variables:
𝑉 = volume; 𝐿 = length; 𝑊 = width; 𝐻 = height
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
Note: The volume of an object that is the same on the top and the bottom is typically
found by determining the area of the two-dimensional base figure and “stretching” that
base to the desired height.
In this case, the base figure is a rectangle with area = 𝐿 × 𝑊, which is multiplied by the
height (𝐻) to get the volume of the figure.
8)
Cone
Volume of the cone:
Variables:
9)
Pyramid with a square base Volume of the pyramid:
Variables:
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
Practice Assignment 11.C
Questions 1 and 2: After doing some work in the house, Bob and Carol want to put a
concrete patio on the side of the house to keep people from tracking mud inside. The
dimensions of the rectangular patio are 23 feet 9 inches by 10 feet 1 inch. The patio will
need to be at least 2 inches deep.
1)
Calculate the volume of concrete needed, in cubic yards, adding 5% to allow for
spillage and an uneven base, and round up to the nearest 1/4 cubic yard. Select
the best answer from the options below.
a)
Order 3.25 yd3
b)
Order 1.75 yd3
c)
Order 3.75 yd3
d)
Order 11.25 yd3
2)
Bob and Carol decide to hire someone to do the patio work. Rachel’s Ready-Mix
bid on the job is based on the information provided. The delivered cost of the
concrete is “$150 per yard (in increments of 1/4-yard) plus a $50 surcharge for
orders less than four yards.” (Concrete companies sometimes advertise “per yard”
when they really mean “per cubic yard.”) Find the total cost of the job to the
nearest cent (tax is already included in the charges and is not charged on the
delivery fee).
Questions 3–5: Recall Carol’s plans to plant 4 tree seedlings in the yard. She wants to
buy bark mulch to place in a circle with a 48-inch diameter around the base of each
tree. She has been told to lay the mulch 3 inches deep. The mulch is sold in bags
containing 2 cubic feet, for $4.49. Calculate the charge for the mulch, including 7.5%
sales tax.
3)
How many cubic feet of mulch does Carol need for the project? Round to the
nearest tenth of a cubic foot.
4)
What is the total charge Carol will have to pay to complete her mulch project?
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
5)
A local nursery is selling a scoop of mulch for $16 and charges $15 to deliver.
What is the total charge Carol will have to pay if she chooses to purchase the
mulch at the nursery instead?
6)
The volume of an object that is the same on the top and the bottom is typically
found by determining the area of the two-dimensional base figure and “stretching”
that base to the desired height. An example of this is the semicircle patio in
Question 1 from the in-class activity. Another example is shown below.
Box
Volume: 𝑉 = 𝐿 × 𝑊 × 𝐻
Variables:
𝑉 = volume; 𝐿 = length; 𝑊 = width; 𝐻 = height
In this case, the base figure is a rectangle (shaded) with area = 𝐿 × 𝑊, which is
multiplied by the height (𝐻) to get the volume of the figure.
Which of the following would be appropriate units of measurement for the different
parts of the figure?
7)
a)
Bottom edge (𝐿), the area of the bottom, and the volume are all measured in
inches.
b)
Bottom edge (𝐿) is measured in square inches; the area of the bottom is
measured in inches and the volume is measured in cubic inches.
c)
Bottom edge (𝐿) is measured in inches; the area of the bottom is measured in
square inches, and the volume is measured in cubic inches.
d)
Bottom edge (𝐿), the area of the bottom and the volume are all measured in
square inches.
The Ko family is going to clean up their yard after a storm. They go to a discount
store to purchase plastic containers for the clean-up. There are a variety of
containers with different shapes and sizes. Help the Ko family calculate the volume
of each container to the nearest cubic inch, assuming the round containers do not
taper.1
1
Sources: http://www.globalindustrial.com/g/office/garbage-recycling/containers-plastic/carlisle-bronco-round-wastecontainers-lids-95672, and http://www.globalindustrial.com/p/office/garbage-recycling/containers-plastic/35-gallonsquare-rubbermaid-waste-receptacle-gray.
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
Containers
Size
1
Volume
1
19 2 inches wide, 19 2 inches long and
5
27 8 inches high
1
1
19 2 inches wide, 19 2 inches long and
1
34 4 inches high
Diameter of 24 inches
1
and 31 inches high
2
4
Diameter of 29 5 inches
and 33 inches high
The following problems should be completed in your binder.
Questions 8–9: The formulas for finding the volume of three-dimensional geometric
figures that occur in everyday use are published in reference books or available online.
Use the web or some other source to find a formula for the volume of each figure.
Define each variable in the formula and label the figure with the variables to indicate the
correct meaning of the variable.
For example:
Box
Volume: 𝑉 = 𝐿 × 𝑊 × 𝐻
Variables:
𝑉 = volume; 𝐿 = length; 𝑊 = width; 𝐻 = height
Note: The volume of an object that is the same on the top and the bottom is typically
found by determining the area of the two-dimensional base figure and “stretching” that
base to the desired height.
In this case, the base figure is a rectangle with area = 𝐿 × 𝑊, which is multiplied by
the height (𝐻) to get the volume of the figure.
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
8)
Cone
Volume of the cone:
Variables:
9)
Pyramid with a square base
Volume of the pyramid:
Variables:
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin