Question

The city government requires that the diameter or longest edge of the new structure not exceed 70 feet. Some members of the DOT think the structure should maximize the total enclosed space, while others think it's more important to maximize the footprint, or floor space. Click each structure to see its dimensions. Use this information to determine which structure you think best meets the requirements and needs. (see picture)

1. What measurement do you need to calculate in order to determine the floor space, or footprint, of each structure?

2. What measurement do you need to calculate in order to determine the amount of space each structure encloses?

3. List the two measurements needed to estimate the amount of material required to cover each structure, not including the floor. Explain how these measurements would be used.

4. Which formula would you use to calculate the floor space of Firm 1's (see picture) structure? Explain your choice. (Use picture)

5. Calculate the floor space of Firm 1's structure.

6. Which formula would you use to calculate the total enclosed space of Firm 1's structure? Explain your choice.

7. What is the total enclosed space of Firm 1's structure? Show your calculations.

8. Write a formula to estimate the amount of material required to cover Firm 1's structure, not including the floor. Explain your reasoning.

9. Use the formula from question 8to estimate the amount of material required to cover Firm 1's structure, not including the floor. Show your calculations.

Answer 1

old question but will answer so this can be closed

1. floor space in this case refers to the area on the bottom face of each structure. for example, since firm 1 is a cylinder, it has a circular base and thus you need to calculate the area of the base

2. "amount of space each structure encloses" is another way to say volume

3. "amount of material required to cover each structure" is the surface area, minus the base, since the floor is not included

Answer 2

4. firm 1 has a circular base as stated earlier, therefore you need the circle area formula (refer to the provided formula sheet)

5. apply the formula with the given dimensions

6. firm 1 is a cylinder, so you'd use the cylinder volume formula (refer to your sheet for the formula)

Answer 3

7. apply the formula

8. use the surface area of a cylinder formula, subtract the area of one circular base since you are not covering the base

9. apply the formula