To estimate the density of a block that is partially submerged in water, we can use the principle of flotation, which states that the weight of the fluid displaced by a floating object is equal to the weight of the object.
If about 30% of the block is submerged in water, this indicates that the block is displacing a volume of water that equals 30% of its own volume.
Since the density of water is approximately 1 g/cm³ (or 1000 kg/m³), we can set up a relationship between the densities. Let \( \rho_{\text{block}} \) be the density of the block.
Using the principle of Archimedes, we have:
\[ \text{Weight of the block} = \text{Weight of water displaced} \]
Let \( V \) be the volume of the block. The weight of the block can be expressed as:
\[ \text{Weight of the block} = \rho_{\text{block}} \times V \times g \]
The weight of the displaced water (30% of the block's volume) is:
\[ \text{Weight of displaced water} = \rho_{\text{water}} \times (0.3V) \times g \]
Setting these two weights equal gives us:
\[ \rho_{\text{block}} \times V \times g = \rho_{\text{water}} \times (0.3V) \times g \]
Since \( g \) and \( V \) are common on both sides, they can be canceled out:
\[ \rho_{\text{block}} = 0.3 \times \rho_{\text{water}} \]
Given that \( \rho_{\text{water}} \approx 1 \text{ g/cm}^3 \):
\[ \rho_{\text{block}} \approx 0.3 \text{ g/cm}^3 \]
Thus, the estimated density of the block is about 0.3 g/cm³.