Task 1
Product: A box of cereal
Dimensions:
Length (l) = 10 inches
Width (w) = 5 inches
Height (h) = 3 inches
Surface Area (SA) = 2lw + 2wh + 2lh
Surface Area = 2(10)(5) + 2(5)(3) + 2(10)(3)
Surface Area = 100 + 30 + 60
Surface Area = 190 square inches
Volume (V) = lwh
Volume = 10 * 5 * 3
Volume = 150 cubic inches
Ratio of surface area to volume = Surface Area/Volume
Ratio = 190/150
Ratio = 19/15
Ratio = 1.27
Therefore, the ratio of surface area to volume for the rectangular prism packaging the cereal is 1.27.
Task 2
a. Time:
Time for John, Rick, and Molli to paint the room together = 4 hours
Time for John to paint the room alone = 6 hours
Time for Rick to paint the room alone = 8 hours
b. Hourly rate for John, Rick, and Molli (working together):
Rooms painted per hour = 1/4 + 1/6 + 1/8
Rooms painted per hour = 6/24 + 4/24 + 3/24
Rooms painted per hour = 13/24 /hour
c. Hourly rate for John:
Rooms painted per hour = 1/6
Hourly rate for John = 6/1
Hourly rate for John = 6 rooms per hour
Hourly rate for Rick:
Rooms painted per hour = 1/8
Hourly rate for Rick = 8/1
Hourly rate for Rick = 8 rooms per hour
d. Equation comparing group rate to sum of individual rates:
Group rate = John's rate + Rick's rate + Molli's rate
13/24 = 6/1 + 8/1 + Molli
13/24 = 14 + Molli
Molli = 13/24 - 14
Molli = -11/24
e. The least common denominator for the equation is 24.
f. Solving the equation:
Molli = -11/24
12 rooms = -11
Molli takes -11/24 hours to paint the room alone, which is not possible.
Task 1
Volume and surface area are often compared by manufacturers in order to
maximize how much of something can go inside of a package (volume) while
keeping how much material is required to create the package (surface area) low.
Pick a product that might be packaged in the shape of a rectangular prism. A
rectangular prism has three dimensions: length, width, and height. The surface
area of a rectangular prism can be found using the formula SA = 2lw + 2wh + 2lh.
The volume of a rectangular prism can be found using the formula V = lwh. Write
an expression for the ratio of surface area to volume for the figure.
Choose an appropriate length, width, and height for your package so that it can fit
the product you are shipping. Using these dimensions, what is the ratio of surface
area to volume?
Task 2
John, Rick, and Molli paint a room together.
a. Pick a reasonable amount of time in which the three friends can paint the
room together. Also pick a reasonable amount of time in which John can
paint the room alone and a reasonable amount of time in which Rick can
paint the room alone.
b. What is the hourly rate for John, Rick, and Molli (when working
together)? Use rooms per hour as the unit for your rates.
c. What is the hourly rate for John? What is the hourly rate for Rick? Refer
to the amount of time you determined in which John and Rick can paint
the room alone. Use rooms per hour as the unit for your rates.
d. Write an equation comparing the group rate to the sum of the individual
rates. How should the group rate and the sum of the individual parts
compare? Use parts (b) and (c) to help you write the equation.
e. What is the least common denominator for the equation you found in part (c)?
f. Solve the equation and determine how long it will take Molli to paint the
room alone.
1 answer