Pit

The pit is 0.8 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 0.6 l of green paint. How many liters of paint are needed when we paint only the sides and bottom of the pit?

Correct answer:

V =  4.1 l

Step-by-step explanation:

$$\begin{gathered} x_0=3\text{m} \\ {y}_0=1.5\text{m} \\ x=1\text{m} \\ y=0.5\text{m} \\ h=0.8\text{m} \\ {h}_1=\sqrt{h^2+((y_0-y)/2{)}^2}=\sqrt{0.8^2+((1.5-0.5)/2{)}^2}\doteq 0.9434\text{m} \\ {h}_2=\sqrt{h^2+((x_0-x)/2{)}^2}=\sqrt{0.8^2+((3-1)/2{)}^2}\doteq 1.2806\text{m} \\ {S}_1=x\cdot y=1\cdot 0.5=\frac{1}{2}=0.5{\text{m}}^2 \\ {S}_2=(x+x_0)\cdot \frac{h_1}{2}=(1+3)\cdot \frac{0.9434}{2}\doteq 1.8868{\text{m}}^2 \\ {S}_3=(y+y_0)\cdot \frac{h_2}{2}=(0.5+1.5)\cdot \frac{1.2806}{2}\doteq 1.2806{\text{m}}^2 \\ S=S_1+2\cdot (S_2+S_3)=0.5+2\cdot (1.8868+1.2806)\doteq 6.8348{\text{m}}^2 \\ V=0.6\cdot S=0.6\cdot 6.8348=4.1\text{l} \end{gathered}$$

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