1. An inground non-diving swimming pool has the following dimensions. It is 33 feet long and 14 feet wide. On the shallow end, it is 3 feet 6 inches deep and slopes gradually to a depth of 5 feet 4 inches. A picture is below. What shape(s) can be used to estimate the volume of the pool.2. What volume formula(s) will be used for the shape listed in number 1.
3. The pool has dimensions that are in both feet and inches. Perform unit conversions on this step.
4. Calculate the approximate volume of the pool.
5. Write the answer from number 4 in scientific notation. It can be approximated.
6. The pool will be filled with standard yellow, number 2 pencils. A typical yellow pencil is about 7.5 inches long and about 0.25 inches across the eraser. What shape(s) can be used to estimate the volume of the pencil.
7. What volume formula(s) will be used for the shape listed in number 5.
8. Calculated the approximate volume a single pencil.
9. Write the answer from number 8 in scientific notation. It can be approximated.
10. Now that the volume for the pencils (number 9) and the pool (number 5) are both known, about how many pencils would it take to fill the pool? Use the scientific notation approximations.
A box with a lid will be made from standard size sheet of office paper, 8.5 inches by 11 inches, by cutting out squares of size x as shown in the picture below. The dotted lines represent where the box will be folded. The lateral faces of the box will overlap.
11. Identify the shape and write the formula that can be used to find the volume of the box.
12. Using the width of the paper (8.5 inches), write an expression to represent the dimension of the box.
13. Using the length of the paper (11 inches), write an expression to represent the dimension of the box. Don’t forget that this box will have both a top and a bottom.
14. What will the height of the box be? Write an expression to represent the entire volume of the box.
15. Use a graphing utility (graphing calculator, Desmos) to find the value of x that will produce the maximum amount of volume. What is the maximum volume? Make sure to label your answer.