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A concrete staircase is to be built. Eachstep is 15 cm high. 25 cm deep, and 1 mwide. The top platform is square. Whatvolume of concrete is needed?

User Carl S
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1 Answer

2 votes

We are going to divide in three parts to find the volume, so the first parte is the rigth one where we have the last step.


\begin{gathered} V_1=(45\operatorname{cm})\cdot(100\operatorname{cm})\cdot(100\operatorname{cm}) \\ =450000cm^3=4500m^3 \end{gathered}

Because we have to take acount the base of the steps not just the steps, now for the second step we have


\begin{gathered} V_2=(30\operatorname{cm})\cdot(100\operatorname{cm})\cdot(25\operatorname{cm}) \\ =75000cm^3=750m^3 \end{gathered}


\begin{gathered} V_2=(30\operatorname{cm})\cdot(100\operatorname{cm})\cdot(25\operatorname{cm}) \\ =75000cm^3=750m^3 \end{gathered}
\begin{gathered} V_3=(15\operatorname{cm})\cdot(100\operatorname{cm})(25\operatorname{cm}) \\ =37500cm^3=375m^3 \end{gathered}

So the total volume is


\begin{gathered} V=V_1+V_2+V_3 \\ =4500m^3\text{ + }750m^3+375m^3=5625m^3 \end{gathered}

The answer is 5625 m3.

And for the fist step we have


\begin{gathered} V_3=(15\operatorname{cm})\cdot(100\operatorname{cm})(25\operatorname{cm}) \\ =37500cm^3=375m^3 \end{gathered}

So the total volume is


\begin{gathered} V=V_1+V_2+V_3 \\ =4500m^3\text{ + }750m^3+375m^3=5625m^3 \end{gathered}

The answer is 5625 m3.

User Roemer
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