Answer:
The total volume of the space inside the steps is 2880 cubic inches.
Step-by-step 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 [tex]16\times 20\times 6 in[/tex]
The volume of the bottom portion is
[tex]V=l\times b\times h\\V=16\times 20\times 6\\V=1920 in^3[/tex]
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
[tex]V=l\times b\times h\\V=20\times 8\times 6\\V=960 in^3[/tex]
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.
