Advertising column

An advertising column has the shape of a triangular prism. The height of the prism is 3.5 metres, and the lengths of the base edges are 1.1 m, 2 m, and 2 m. The lateral surface of the prism forms the advertising space. The town pays 35,000 CZK for its production and installation. The town charges a fee of 3 CZK per dm² per week. Calculate how many weeks it will take for the town to recover the amount paid, assuming the surface on the column is fully utilised.

Final Answer:

n =  6.5359

Step-by-step explanation:

$$\begin{gathered} h=3.5\text{m} \\ a=1.1\text{m} \\ b=2\text{m} \\ c=2\text{m} \\ P=35000\text{Kc} \\ z=3{\text{Kc/dm}}^2 \\ S=(a+b+c)\cdot h=(1.1+2+2)\cdot 3.5=\frac{357}{20}=17\frac{17}{20}=17.85{\text{m}}^2 \\ {S}_1=1{\text{dm}}^2\to {\text{m}}^2=1:100{\text{m}}^2=0.01{\text{m}}^2 \\ {n}_1=S/S_1=17.85/0.01=1785 \\ t=z\cdot n_1=3\cdot 1785=5355\text{Kc/w} \\ n=P/t=35000/5355=6.5359 \end{gathered}$$

Try another example