Atheater 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?

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

The volume of the bottom portion is

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

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.

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation: