The square

The square oak board (with density ρ = 700 kg/m³) has a side length of 50 cm and a thickness of 30 mm. 4 holes with a diameter of 40 mm are drilled into the board. What is the weight of the board?

Final Answer:

m =  5.14 kg

Step-by-step explanation:

$$\begin{gathered} \rho =700{\text{kg/m}}^3 \\ a=50\text{cm} \\ h=30\text{mm}\to \text{cm}=30:10\text{cm}=3\text{cm} \\ n=4 \\ D=40\text{mm}\to \text{cm}=40:10\text{cm}=4\text{cm} \\ {V}_1=a\cdot a\cdot h=50\cdot 50\cdot 3=7500{\text{cm}}^3 \\ r=D/2=4/2=2\text{cm} \\ {V}_2=\pi \cdot r^2\cdot h=3.1416\cdot 2^2\cdot 3\doteq 37.6991{\text{cm}}^3 \\ V=V_1-n\cdot V_2=7500-4\cdot 37.6991\doteq 7349.2036{\text{cm}}^3 \\ {\rho }_2=\rho \to {\text{g/cm}}^3=\rho :1000{\text{g/cm}}^3=700:1000{\text{g/cm}}^3=0.7{\text{g/cm}}^3 \\ {m}_2={\rho }_2\cdot V=0.7\cdot 7349.2036\doteq 5144.4425\text{g} \\ m=m^2\to \text{kg}=m^2:1000\text{kg}=5144.4425:1000\text{kg}=5.14\text{kg}=5.14\text{kg} \end{gathered}$$

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