How you calculate the volume of steps?

Answer 1

It depends on whether the steps are completed underneath or hollow. I assume it's like a block of steps filled in completely underneath each step.

When the steps are filled in from the floor up, they are a series of cuboids. If we look at the steps side on and imagine lines vertically downwards between the steps, it's like a series of rectangles getting progressively larger. We can calculate the area of each rectangle by multiplying the length by the width as usual. Then if we add the sizes together we have the surface area of the side face of the steps. Then we can just multiply by the width of each step to calculate the volume of the steps.

A simple formula can be found for the area of any steps, but it's probably better to understand how it works.

Call the width of each step w. Call the depth of each step, that's how far back each one goes before you reach the next, d. And the heights of each step off the floor can be called h1, h2, h3...

The formula for the volume of the steps is therefore:

(h1 + h2 + h3 +...)*d*w