a staircase has stairs with a width of 11 inches and a height of 8 inches per step. a storage closet is to be built under the staircase between the 5th and 13th steps.

1. draw a model of the back wall of the closet showing the stairs.

2. if the ceiling of the closet is the bottom of the stairs, what is the area of back wall of the closet?

3. if the length of the step is 38 inches, then what is the volume of the closet?

4. instead, if a board is placed over the bottom of the stairs so that the top of the closet is flat but slanted, draw a new model of the back wall of the closet.

5. using geometry formulas, find the area of the back wall of the closet.

6. find an equation for the position of the board. use calculus to find the area of the back wall of the closet.

7. if the length of the step is 38 inches, the what is the volume of the closet with slanted ceiling?