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. Task 3
Suppose you are having a birthday party at the local bowling alley. You are trying to figure out how many people you can afford to invite.
a. The number of guests you can invite to your party varies inversely with the price per bowler at the alley. Explain what this means.
b. How much money are you willing to spend to host this bowling party?
c. Set up an equation that shows the inverse relationship between the number of guests at your party and the price per bowler. Your answer to part (b) should be part of this equation.
d. Research two local bowling alleys. Record the price per bowler at each of these two alleys.
Calculate how many guests you will be able to invite to your party at each of the bowling alleys. Which alley would you choose for your party? Why?