We are given the formula for density:

$D = \frac{M}{V}$

where:

• $D$ is the density,
• $M$ is the mass,
• $V$ is the volume.

Part (a)

We are asked to calculate the density of a metal block with:

• Mass $M = 30 \, \text{g}$,
• Volume $V = 5 \, \text{cm}^3$.

Using the formula for density:

$D = \frac{M}{V} = \frac{30 \, \text{g}}{5 \, \text{cm}^3} = 6 \, \text{g/cm}^3$

Thus, the density of the block is $6 \, \text{g/cm}^3$.

Part (b)

We are given:

• Volume $V = 12 \, \text{cm}^3$,
• Density $D = 18 \, \text{g/cm}^3$.

We need to find the mass $M$. Using the formula $D = \frac{M}{V}$, we can rearrange it to solve for $M$:

$M = D \times V$

Substitute the given values:

$M = 18 \, \text{g/cm}^3 \times 12 \, \text{cm}^3 = 216 \, \text{g}$

Thus, the mass of the block is $216 \, \text{g}$.

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Would you like further details on how the formula was derived or any related concepts?

Here are 5 related questions to consider:

1. How does the unit of density change if mass is measured in kilograms instead of grams?
2. What would be the volume of a block with a mass of 50 g and a density of 10 g/cm³?
3. If the density of a block is doubled but the volume stays constant, how does the mass change?
4. What are the common units of density in the metric and imperial systems?
5. How can density help in identifying unknown materials?

Tip: The higher the density of an object, the more mass it contains within a given volume.