A wooden block measuring 40 cm x 10 cm x 5 cm has a mass 850 g. Find the density of 3 wood.
The Correct Answer and Explanation is:
To find the density of the wood, we can use the formula: Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}Density=VolumeMass
Step 1: Calculate the volume of the wooden block
The dimensions of the wooden block are given as:
- Length = 40 cm
- Width = 10 cm
- Height = 5 cm
The volume of the block can be calculated using the formula for the volume of a rectangular prism: Volume=Length×Width×Height\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}Volume=Length×Width×Height
Substitute the given values: Volume=40 cm×10 cm×5 cm\text{Volume} = 40 \, \text{cm} \times 10 \, \text{cm} \times 5 \, \text{cm}Volume=40cm×10cm×5cm Volume=2000 cm3\text{Volume} = 2000 \, \text{cm}^3Volume=2000cm3
Step 2: Convert mass to kilograms
The mass of the block is 850 g. To ensure consistency in units, let’s convert this mass to kilograms: Mass=850 g=0.850 kg\text{Mass} = 850 \, \text{g} = 0.850 \, \text{kg}Mass=850g=0.850kg
Step 3: Calculate the density
Now, we can use the formula for density. We already have the mass in kilograms and the volume in cubic centimeters, but since we want the density in kg/m3\text{kg/m}^3kg/m3, we need to convert the volume from cm³ to m³.
1 m³ = 1,000,000 cm³, so: Volume in m3=2000 cm31,000,000=0.002 m3\text{Volume in m}^3 = \frac{2000 \, \text{cm}^3}{1,000,000} = 0.002 \, \text{m}^3Volume in m3=1,000,0002000cm3=0.002m3
Now, substitute the mass and volume into the density formula: Density=0.850 kg0.002 m3\text{Density} = \frac{0.850 \, \text{kg}}{0.002 \, \text{m}^3}Density=0.002m30.850kg Density=425 kg/m3\text{Density} = 425 \, \text{kg/m}^3Density=425kg/m3
Conclusion:
The density of the wood is 425 kg/m³.
This means that for every cubic meter of this particular wood, the mass is 425 kg. The density gives an idea of how compact the material is. In this case, the relatively low density suggests that the wood is not particularly dense, which is typical for many types of wood.
