Small tower 2

A small tower has a square floor plan with a side length of 5 m. The tower's roof has the shape of a regular quadrilateral pyramid (without the base) with a height of 8 m. During renovation, the roof will be covered with new tiles. 11 tiles are used per 1 m². One pallet holds 240 tiles. Calculate the minimum number of pallets of roof tiles that will need to be ordered.

Final Answer:

n =  4

Step-by-step explanation:

$$\begin{gathered} a=5\text{m} \\ h=8\text{m} \\ {n}_1=111{\text{/m}}^2 \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{8^2+(5/2{)}^2}\doteq 8.3815\text{m} \\ {S}_1=\frac{a\cdot h_2}{2}=\frac{5\cdot 8.3815}{2}\doteq 20.9538{\text{m}}^2 \\ S=4\cdot S_1=4\cdot 20.9538=5\sqrt{281}{\text{m}}^2\doteq 83.8153{\text{m}}^2 \\ N=S\cdot n_1=83.8153\cdot 11=55\sqrt{281}\doteq 921.968 \\ {n}_2=N/240=921.968/240\doteq 3.8415 \\ n=\lceil n_2\rceil =\lceil 3.8415\rceil =4 \end{gathered}$$

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