A rectangular block of copper metal weighs 1896 grams and dimensions of the block are 8.4 CM by 5.5 cm by 4.6 cm what the density
The Correct Answer and Explanation is:
Correct Answer:
To find the density of the copper block, we use the formula:Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}Density=VolumeMass
Step 1: Given Values
- Mass = 1896 grams
- Dimensions:
Length = 8.4 cm
Width = 5.5 cm
Height = 4.6 cm
Step 2: Calculate the Volume
Volume=Length×Width×Height\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}Volume=Length×Width×HeightVolume=8.4×5.5×4.6=212.52 cm3\text{Volume} = 8.4 \times 5.5 \times 4.6 = 212.52\ \text{cm}^3Volume=8.4×5.5×4.6=212.52 cm3
Step 3: Calculate the Density
Density=1896212.52≈8.92 g/cm3\text{Density} = \frac{1896}{212.52} \approx 8.92\ \text{g/cm}^3Density=212.521896≈8.92 g/cm3
Final Answer: 8.92 grams per cubic centimeter
Explanation:
Density is a physical property that describes how much mass is packed into a unit volume of a material. It is expressed as mass per unit volume, usually in grams per cubic centimeter for solids. In this case, we are given a rectangular block of copper metal and asked to find its density. The information provided includes the mass and the dimensions of the block.
The mass of the copper block is 1896 grams. Since it is a rectangular block, we can easily calculate the volume using the formula for the volume of a rectangular prism, which is length multiplied by width multiplied by height. Plugging in the given dimensions (8.4 cm, 5.5 cm, and 4.6 cm), we calculate the volume to be 212.52 cubic centimeters.
Once we have both mass and volume, we divide the mass by the volume to find the density. The result is approximately 8.92 grams per cubic centimeter. This is very close to the known standard density of copper, which is about 8.96 grams per cubic centimeter. Small differences may be due to rounding or measurement tolerance.
Density helps in identifying substances and understanding material properties. For example, knowing the density of copper helps engineers and scientists determine whether an object is made of pure copper or a mixture. In industrial and academic settings, such density measurements are crucial for quality control and scientific research.
