Calculate 81553

The picture puzzle made of wooden cubes weighs 0.792 kg. One cube has an edge length of 4 cm and a weight of 33 grams. Find out how many cubes make up a puzzle and calculate the wood density in kg/m³.

Correct answer:

n =  24
ρ =  515.625 kg/m³

Step-by-step explanation:

$$\begin{gathered} m=0.792\text{kg}\to \text{g}=0.792\cdot 1000\text{g}=792\text{g} \\ a=4\text{cm} \\ {m}_1=33\text{g} \\ n=m/m_1=792/33=24 \end{gathered}$$

$$\begin{gathered} V_1=a^3=4^3=64{\text{cm}}^3 \\ {\rho }_1=m_1/V_1=33/64=\frac{33}{64}\doteq 0.5156{\text{g/cm}}^3 \\ \rho ={\rho }_1\to {\text{kg/m}}^3={\rho }_1\cdot 1000{\text{kg/m}}^3=0.5156\cdot 1000{\text{kg/m}}^3=515.625{\text{kg/m}}^3=515.625{\text{kg/m}}^3 \end{gathered}$$

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