How much cement do I need for a staircase?

[Chrissy19]

Suppose that you wish to construct the staircase pictured below by building a form out of wood and then filling it with cement.

• How much cement do you need?

Once the staircase has hardened you will paint the steps and the sides, but not the base or the back.

• If each can of paint covers 15 square feet, how many cans of paint should you purchase?

 

[Chrissy19]

 

[MarkFL]

To find the volume, I would divide this object into 3 rectangular prisms...I can see two ways to do this. Then add the volumes of the 3 prisms to get the total volume.

 

[Aliabla]

I mean usually would you just not use this to find the volume of the staircase, equation volume=length x width x height. Your length, width, and height values are all displayed in the diagram.


So the volume of one step is [MATH]length \times width \times height[/MATH] Length of one step is shown or can simply be worked out from [MATH]91.44cm / 3[/MATH] which is just 30.48.

 

[Dr.Peterson]

I mean usually would you just not use this to find the volume of the staircase, equation volume=length x width x height. Your length, width, and height values are all displayed in the diagram.


So the volume of one step is [MATH]length \times width \times height[/MATH] Length of one step is shown or can simply be worked out from [MATH]91.44cm / 3[/MATH] which is just 30.48.

That's the formula for a single rectangular prism, whose faces are all rectangles.. This can be thought of as only part of one, or as made up of several of them.

I would observe that the staircase can be made from 6 identical blocks, each 64.21 by 30.48 by 30.48.

Then, for the area to be painted, you can just find the area of each individual face and add them up. The sides can be made from 6 identical squares, or from 3 different rectangles.

 

[Chrissy19]

Thank you I confused myself by separating them into 3 separate prisms but though that 91.44 would change as the prisms became smaller.

 

[Dr.Peterson]

Thank you I confused myself by separating them into 3 separate prisms but thought that 91.44 would change as the prisms became smaller.

Actually, it does change; there is no way to split the shape into 3 prisms that all have that height. They will have different heights, or else the same (smaller) height and different widths.

How did you divide it? Can you describe or show the three pieces you used?

 

[Otis]

How much cement …

Hi Chrissy. That's a question about volume. Can you see that the staircase structure is made up of six identical rectangular blocks? Each block measures 30.48 by 30.48 by 64.21 units.

Use the volume formula for a rectangular solid, to calculate the volume of these blocks. (If you need the formula, it ought to be in your textbook. Look under 'volume', in the index.)

Please also complete the request to read the forum's guidelines. (You forgot to show some work and to explain why you're stuck.) Thank you!

?

 

[MarkFL]

I could swear I saw this question just today in another thread...

 

[pka]

Suppose that you wish to construct the staircase pictured below by building a form out of wood and then filling it with cement.

• How much cement do you need?

Once the staircase has hardened you will paint the steps and the sides, but not the base or the back.

• If each can of paint covers 15 square feet, how many cans of paint should you purchase?View attachment 13875

You must consider the volume of a solid: \(\displaystyle V=(91.44)(91.44)(64.21)\).
Now remove the volume of two steps: \(\displaystyle 2(30.48)(64.21)\)
Doing those calculations and taking the difference what do you get?