Question

A theater wants to build movable steps that they can use to go on and off the stage. The dimesions are 12 in, 16 in, 20 in, 6 in, and 8 in. 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

The total volume of the space inside the steps is 2880 cubic inches.

Explanation:

Given : A theater wants to build movable steps that they can use to go on and off the stage. The dimensions are 12 in, 16 in, 20 in, 6 in, and 8 in. They want the steps to have enough space inside so they can also be used to store props.

To find : How much space is inside the steps?

Solution :

According to question,

The image form of store props is a prism split into two rectangular prism.

Refer the attached figure below.

The bottom portion of the steps having dimension
`16* 20* 6 in`

The volume of the bottom portion is

`V=l* b* h\\V=16* 20* 6\\V=1920 in^3`

The top part have a width of 8 inches as entire width of bottom is 16 inches.

Length is 20 inches.

Height of the steps is 6 inches as total height is 12 inches.

The volume of the top part is

`V=l* b* h\\V=20* 8* 6\\V=960 in^3`

So, the total volume of the space inside the steps is

1920+960 = 2880 cubic inches.

Therefore, The total volume of the space inside the steps is 2880 cubic inches.