A metal block having an internal cavity weight 110 g in air and 80 g in water. If the density of metal is 5.5 g//cc, then the volume of cavity is :

Options

A. 30cc
B. 20 cc
C. 10 cc
D. 5 cc

Explanation

To find the volume of the cavity in the metal block, we can follow these steps:

### Step 1: Determine the weight of the liquid displaced
The weight of the metal block in air is given as 110 g, and its weight in water is 80 g. The difference in weight gives us the weight of the liquid displaced.

\[ \text{Weight of liquid displaced} = \text{Weight in air} - \text{Weight in water} = 110 \, \text{g} - 80 \, \text{g} = 30 \, \text{g} \]

### Step 2: Calculate the volume of liquid displaced
The volume of liquid displaced can be calculated using the formula:

\[ \text{Volume of liquid displaced} = \frac{\text{Weight of liquid displaced}}{\text{Density of water}} \]

Assuming the density of water is \(1 \, \text{g/cm}^3\):

\[ \text{Volume of liquid displaced} = \frac{30 \, \text{g}}{1 \, \text{g/cm}^3} = 30 \, \text{cm}^3 \]

### Step 3: Calculate the actual volume of the metal block
The actual volume of the metal block can be calculated using its mass and density. The density of the metal is given as \(5.5 \, \text{g/cm}^3\).

\[ \text{Actual volume of block} = \frac{\text{Mass of block}}{\text{Density of metal}} = \frac{110 \, \text{g}}{5.5 \, \text{g/cm}^3} = 20 \, \text{cm}^3 \]

### Step 4: Determine the volume of the cavity
The volume of the cavity can be found by subtracting the actual volume of the block from the volume of the liquid displaced.

\[ \text{Volume of cavity} = \text{Volume of liquid displaced} - \text{Actual volume of block} = 30 \, \text{cm}^3 - 20 \, \text{cm}^3 = 10 \, \text{cm}^3 \]

### Final Answer
The volume of the cavity is \(10 \, \text{cm}^3\).

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