Pit

The pit is 1.2 m deep and in the shape of a truncated pyramid with a rectangular base. Its length and width are the top 3 × 1.5 m and the bottom 1 m × 0.5 m. To paint one square meter of the pit, we use 0.8 l of green paint. How many liters of paint are needed when we paint only the sides and bottom of the pit?

Final Answer:

V =  7.06 l

Step-by-step explanation:

$$\begin{gathered} x_0=3\text{m} \\ {y}_0=1.5\text{m} \\ x=1\text{m} \\ y=0.5\text{m} \\ h=1.2\text{m} \\ {h}_1=\sqrt{h^2+((y_0-y)/2{)}^2}=\sqrt{1.2^2+((1.5-0.5)/2{)}^2}=\frac{13}{10}=1.3\text{m} \\ {h}_2=\sqrt{h^2+((x_0-x)/2{)}^2}=\sqrt{1.2^2+((3-1)/2{)}^2}\doteq 1.562\text{m} \\ {S}_1=x\cdot y=1\cdot 0.5=\frac{1}{2}=0.5{\text{m}}^2 \\ {S}_2=(x+x_0)\cdot \frac{h_1}{2}=(1+3)\cdot \frac{1.3}{2}=\frac{13}{5}=2.6{\text{m}}^2 \\ {S}_3=(y+y_0)\cdot \frac{h_2}{2}=(0.5+1.5)\cdot \frac{1.562}{2}\doteq 1.562{\text{m}}^2 \\ S=S_1+2\cdot (S_2+S_3)=0.5+2\cdot (2.6+1.562)\doteq 8.8241{\text{m}}^2 \\ V=0.8\cdot S=0.8\cdot 8.8241=7.06\text{l} \end{gathered}$$

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