A solid body of mass `82` g and volume `91.1 "cm"^(3)` is put into water . Its density is `x//10"g cm"^(-3)` , then find `x` .

Explanation

To find the value of \( x \) in the given problem, we need to follow these steps:

### Step 1: Write down the given data
- Mass of the solid body, \( m = 82 \, \text{g} \)
- Volume of the solid body, \( V = 91.1 \, \text{cm}^3 \)

### Step 2: Calculate the density of the solid body
Density (\( \rho \)) is calculated using the formula:
\[ \rho = \frac{m}{V} \]
Substituting the values:
\[ \rho = \frac{82 \, \text{g}}{91.1 \, \text{cm}^3} \]

### Step 3: Perform the division
Now, calculate the density:
\[ \rho \approx 0.9011 \, \text{g/cm}^3 \]
For simplicity, we can round this to:
\[ \rho \approx 0.9 \, \text{g/cm}^3 \]

### Step 4: Express the density in the form given in the question
The problem states that the density can be expressed as:
\[ \rho = \frac{x}{10} \, \text{g/cm}^3 \]
We can rewrite \( 0.9 \, \text{g/cm}^3 \) as:
\[ 0.9 = \frac{9}{10} \, \text{g/cm}^3 \]

### Step 5: Set the two expressions for density equal to each other
Now we can set the two expressions for density equal:
\[ \frac{x}{10} = \frac{9}{10} \]

### Step 6: Solve for \( x \)
To find \( x \), we can multiply both sides by 10:
\[ x = 9 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{9} \]

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