A block of metal has a volume of 13.8 in3in3 and weighs 5.32 lblb. What is its density in grams per cubic centimeter?

Express the density in grams per cubic centimeter to three significant figures.

To calculate the density of the metal block, we need to use the formula for density:

\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]

### Step 1: Convert the weight to grams
We are given the weight of the block in pounds (5.32 lb). Since 1 pound is equivalent to 453.592 grams, we can convert the mass:

\[
5.32 \, \text{lb} \times 453.592 \, \frac{\text{g}}{\text{lb}} = 2412.09 \, \text{g}
\]

### Step 2: Convert the volume to cubic centimeters
We are given the volume in cubic inches (13.8 in³). Since 1 cubic inch is equal to 16.387 cubic centimeters, we convert the volume:

\[
13.8 \, \text{in}^3 \times 16.387 \, \frac{\text{cm}^3}{\text{in}^3} = 226.145 \, \text{cm}^3
\]

### Step 3: Calculate the density
Now that we have both the mass in grams and the volume in cubic centimeters, we can calculate the density:

\[
\text{Density} = \frac{2412.09 \, \text{g}}{226.145 \, \text{cm}^3} = 10.66 \, \frac{\text{g}}{\text{cm}^3}
\]

Thus, the density of the metal block is **10.66 g/cm³**.

Do you need more details or have any other questions?

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Here are 5 related questions:
1. How would the density change if the volume was halved but the mass remained constant?
2. What is the density of another object with the same mass but a volume of 30 cm³?
3. How do you convert between pounds per cubic inch and grams per cubic centimeter?
4. How does temperature affect the density of metals?
5. Can you compare the density of this metal with that of water, which is 1 g/cm³?

**Tip:** Always remember to convert all units to the same system when calculating quantities like density!

A block of metal has a volume of 13.8 in³ and weighs 5.32 lb. What is its density in grams per cubic centimeter? Express the density in grams per cubic centimeter to three significant figures.

Learn how to calculate the density of a metal block with a mass of 5.32 lb and a volume of 13.8 in³. This problem demonstrates the key concepts of unit conversion and density calculation. Suitable for students in Grades 9-12.

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