Quadrilateral 44731

The pit for ecological waste has the shape of a regular quadrilateral prism. The supporting edge is 5 meters long. The depth of the pit is 3.5 m. The company enlarged the pit by extending the base edges by 50 cm. By how much m³ has the amount of waste that can fit in the pit increased?

Final Answer:

x =  18.375 m³

Step-by-step explanation:

$$\begin{gathered} a=5\text{m} \\ h=3.5\text{m} \\ c=50\text{cm}\to \text{m}=50:100\text{m}=0.5\text{m} \\ b=a+c=5+0.5=\frac{11}{2}=5.5\text{m} \\ {V}_1=a^2\cdot h=5^2\cdot 3.5=\frac{175}{2}=87.5{\text{m}}^3 \\ {V}_2=b^2\cdot h=5.5^2\cdot 3.5=\frac{847}{8}=105.875{\text{m}}^3 \\ x=V_2-V_1=105.875-87.5=18.375{\text{m}}^3 \end{gathered}$$

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