Question

A theater wants to build movable steps that they can use to go on and off the stage. They want the steps to have enough space inside so they can also be used to store props. How much space is inside the steps?

Answer 1

Answer:

2880 in³

Step-by-step explanation:

We can first split this prism into two rectangular prisms.  The first one, the bottom portion of the steps, will have dimensions 16 in x 20 in x 6 in; this makes the volume

16(20)(6) = 1920 in³

The top part have a width of 8 inches.  This is because the entire width of the bottom is 16; the part from where the top step ends to the other side is 8 inches of it.  This leaves 16-8 = 8 inches for the width.

The length will be 20, just as the length of the entire set of steps is.

The height will be 6; this is because the total height of the steps is 12 inches, and the height of only the bottom step is 6; this leaves 12-6 = 6 steps.

This gives us 8 in x 20 in x 6 in, giving us

8(20)(6) = 960 in³

This makes the total volume

1920+960 = 2880 in³