Whitewashed 3483

The pool is in the shape of a vertical prism with a bottom in the shape of an isosceles trapezoid with dimensions of the bases of the trapezoid 10m and 18m, and arms 7m are 2m deep. During spring cleaning, the bottom and walls of the pool must be whitewashed. How much m² needs to be whitewashed?

Correct answer:

S =  164.4239 m²

Step-by-step explanation:

$$\begin{gathered} a=10 \\ c=18 \\ r=7 \\ h=2 \\ o=a+c+2\cdot r=10+18+2\cdot 7=42 \\ {S}_1=o\cdot h=42\cdot 2=84 \\ {h}_1=\sqrt{r^2-((a-c)/2{)}^2}=\sqrt{7^2-((10-18)/2{)}^2}=\sqrt{33}\doteq 5.7446 \\ {S}_2=(a+c)\cdot h_1/2=(10+18)\cdot 5.7446/2=14\sqrt{33}\doteq 80.4239 \\ S=S_1+S_2=84+80.4239=164.4239{\text{m}}^2 \end{gathered}$$

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