Foundations of Mathematical Reasoning
Student Assignment 3.2.C
Assignment 3.2 Part C
1) 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.
Part A: 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:
Answer choices:
a) Order 1.25 yd3
b) Order 1.75 yd3
c) Order 3.75 yd3
d) Order 11.25 yd3
Part B: Bob and Carol decide to hire someone to do the patio work. Rachel’s Ready-Mix bid on
the job 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).
Answer blank:
The total cost of the job is $_________.
2) 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
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Foundations of Mathematical Reasoning
Student Assignment 3.2.C
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% tax.
Part A: To the nearest foot, how many cubic feet of mulch does Carol need for the
project?
Answer blank:
Carol needs ______ cubic feet of mulch for the project.
Part B: To the nearest cent, what is the total charge Carol will have to pay to complete
her mulch project?
Answer blank:
Carol will have to pay $________ to complete her mulch project.
3) 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. The semicircle patio in Question 1 from the lesson is an
example of this. 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.
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Foundations of Mathematical Reasoning
Student Assignment 3.2.C
Which of the following would be appropriate units of measurement for the different parts
of the figure?
Answer choices:
a) Bottom edge (L), the area of the top, and the volume are all measured in inches.
b) Bottom edge (L) is measured in square inches; the area of the top is measured in
inches and the volume is measured in cubic inches.
c) Bottom edge (L) is measured in inches; the area of the top is measured in square
inches, and the volume is measured in cubic inches.
d) Bottom edge (L), the area of the top and the volume are all measured in square
inches.
4) The formula for the area of a circle is given below. Select the statements from the list
below that are true. There may be more than one correct answer.
A = pr2
Answer choices:
a) A is called a constant because it always represents area.
b) A is called a variable because it can represent different values.
c) p is called a constant because it always represents the same value,
approximately 3.14.
d) p is called a variable because it can represent different values.
The following problems should be printed, completed, and placed in
your binder:
Questions 5 and 6: The formulas for finding the volume of three-dimensional
geometric figures that occur in everyday use are published in reference books or
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Foundations of Mathematical Reasoning
Student Assignment 3.2.C
available online. Use the Internet or some other reliable 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.
5) Cylinder
Volume of the cylinder:
Variables:
6) Pyramid with a square base
Volume of the pyramid:
Variables:
HINTS (Note not all questions will have hints)
Hint #1: Refer to Resource Dimensional Analysis, if needed.
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Foundations of Mathematical Reasoning
Student Assignment 3.2.C
Hint #2: It may be helpful to draw a picture.
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