A pebble of mass 33 g is lowered into a measuring jar containing water so that it is completely covered in water. The initial level of water was 60 ml and after lowering the stone it was found to be 74 ml. What is the density of stone?

Answer

To find the density of the pebble, we will follow these steps:

### Step 1: Identify the mass of the pebble.
The mass of the pebble is given as 33 grams.

### Step 2: Determine the initial and final water levels.
The initial level of water in the measuring jar is 60 ml, and after lowering the pebble, the final level of water is 74 ml.

### Step 3: Calculate the change in water level.
To find the volume of the pebble, we need to calculate the change in water level:
\[ \text{Change in water level} = \text{Final level} - \text{Initial level} = 74 \, \text{ml} - 60 \, \text{ml} = 14 \, \text{ml} \]

### Step 4: Relate the change in water level to the volume of the pebble.
The change in water level (14 ml) is equal to the volume of the pebble. Therefore, the volume of the pebble is 14 ml, which is equivalent to 14 cm³ (since 1 ml = 1 cm³).

### Step 5: Use the formula for density.
Density is defined as mass divided by volume:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{33 \, \text{g}}{14 \, \text{cm}^3} \]

### Step 6: Calculate the density.
Now, we perform the division:
\[ \text{Density} = \frac{33}{14} \approx 2.36 \, \text{g/cm}^3 \]

### Final Answer:
The density of the stone is approximately **2.36 g/cm³**.

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