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. They want the steps to have enough space inside so they can also be used to store props 16 in, 8 in, 6 in, 20 in, 12 in.

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.

2880 in³

Step-by-step explanation:

Complete question: How much space is inside the steps?

SOLUTION:

See attachment for the figure.

Firstly, split this prism into two rectangular prisms. The first one, the bottom portion of the steps, will have dimensions of 16 in x 20 in x 6 in i.e 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.

Therefore, 16-8 = 8 inches for the width.

The length will be 20, similarly as the length of the whole arrangement 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

Thus, the total volume :

1920+960 = 2880 in³

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

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