If two cubes made of iron, each of side 10 mm are dropped in a tumbler containing 200 c.c. of water, what will be the net volume (in ml) of the contents of the tumbler ?

Options

A. A. 200002
B. B. 200001
C. C. 202
D. D. 201

Answer

To solve the problem, we need to calculate the net volume of the contents of the tumbler after dropping two iron cubes into it. Here’s the step-by-step solution:

### Step 1: Calculate the volume of one cube
The formula for the volume \( V \) of a cube is given by:
\[ V = \text{side}^3 \]
Given that the side of each cube is 10 mm, we can calculate the volume of one cube:
\[ V = 10 \, \text{mm} \times 10 \, \text{mm} \times 10 \, \text{mm} = 1000 \, \text{mm}^3 \]

### Step 2: Calculate the volume of two cubes
Since there are two cubes, we multiply the volume of one cube by 2:
\[ \text{Volume of two cubes} = 2 \times 1000 \, \text{mm}^3 = 2000 \, \text{mm}^3 \]

### Step 3: Convert the volume of the cubes to cubic centimeters
We know that:
\[ 1 \, \text{cm}^3 = 1000 \, \text{mm}^3 \]
To convert the volume of the cubes from mm³ to cm³:
\[ \text{Volume in cm}^3 = \frac{2000 \, \text{mm}^3}{1000} = 2 \, \text{cm}^3 \]

### Step 4: Calculate the total volume of water in the tumbler
The initial volume of water in the tumbler is given as 200 cm³.

### Step 5: Calculate the net volume in the tumbler
Now, we add the volume of the water and the volume of the two cubes:
\[ \text{Net Volume} = \text{Volume of water} + \text{Volume of two cubes} \]
\[ \text{Net Volume} = 200 \, \text{cm}^3 + 2 \, \text{cm}^3 = 202 \, \text{cm}^3 \]

### Step 6: Convert the net volume to milliliters
Since \( 1 \, \text{cm}^3 = 1 \, \text{ml} \):
\[ \text{Net Volume in ml} = 202 \, \text{cm}^3 = 202 \, \text{ml} \]

### Final Answer
The net volume of the contents of the tumbler is **202 ml**.

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