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Proof 6: Prism and cylinder volume

In a room with 3 metres to the ceiling, there are 3 cubic metres above each square metre floor regardless of the shape. The 3 cubic metres are multiplied with the number of square metres. Is the floor edged, then it is a prism-shape:

$$A_\text{prism}= A_\text{base}h\quad_\blacksquare $$

Is the floor circle-shaped, then it is a cylinder-shape (a column):

$$A_\text{cylinder}= \underbrace{A_\text{base}}_\text{circle}h=\pi r^2 h\quad_\blacksquare \qquad\leftarrow \text{ Circle area, } A=\pi r^2 $$

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