A rectangular block of substance X has a length of 20 cm, breadth 10 cm and height 5 cm. The mass of the block is 2.7 kg. If density of water is 1 g/`cm^(3)` then, which of the following statements is correct?

Options

A. The block will float in water as its density is 0.027 g/`cm^(3)`.
B. The block will sink in water as its density is 2.7 g/`cm^(3)`
C. The block will sink in water as its density is 2.7 kg/`cm^(3)`
D. The block will float in water as its density is 0.0027 g/`cm^(3)`

Explanation

To determine the correct statement regarding the rectangular block of substance X, we need to calculate its density and compare it with the density of water.

### Step 1: Calculate the volume of the block
The volume \( V \) of a rectangular block can be calculated using the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Given:
- Length = 20 cm
- Breadth = 10 cm
- Height = 5 cm

Substituting the values:
\[ V = 20 \, \text{cm} \times 10 \, \text{cm} \times 5 \, \text{cm} \]
\[ V = 1000 \, \text{cm}^3 \]

### Step 2: Calculate the density of the block
Density \( \rho \) is defined as mass per unit volume:
\[ \rho = \frac{\text{mass}}{\text{volume}} \]
Given:
- Mass = 2.7 kg = 2700 g (since 1 kg = 1000 g)

Now substituting the values:
\[ \rho = \frac{2700 \, \text{g}}{1000 \, \text{cm}^3} \]
\[ \rho = 2.7 \, \text{g/cm}^3 \]

### Step 3: Compare the density of the block with the density of water
The density of water is given as:
- Density of water = 1 g/cm³

Now we compare:
- Density of the block \( \rho = 2.7 \, \text{g/cm}^3 \)
- Density of water = 1 g/cm³

Since the density of the block (2.7 g/cm³) is greater than the density of water (1 g/cm³), the block will sink in water.

### Conclusion
The correct statement is that the block will **not float** in water because its density is greater than that of water.