To find the value of C, we first need to determine the value of B. The problem states that B is the sum of the first three even natural numbers.

Calculating the Value of B

The first three even natural numbers are 2, 4, and 6.

Therefore, the value of B is:

B = 2 + 4 + 6

B = 12

Understanding Third Proportional

The problem states that C is the third proportional of 44 and B. This means that the ratio between the first number (44) and the second number (B) is the same as the ratio between the second number (B) and the third number (C).

Mathematically, this can be represented as:

$$ \frac{44}{B} = \frac{B}{C} $$

Calculating the Value of C

We can rearrange the formula to solve for C:

$$ C = \frac{B \times B}{44} $$

Now, substitute the value of B which we found to be 12:

$$ C = \frac{12 \times 12}{44} $$

$$ C = \frac{144}{44} $$

Performing the Division and Rounding

To find the numerical value of C, we divide 144 by 44:

$$ C \approx 3.272727... $$

The question asks to round the answer to two decimal places.

Rounding 3.272727... to two decimal places gives us 3.27.

Final Answer Verification

The calculated value of C is approximately 3.27, which matches one of the given options.