Determine the approximate value that should replace the question mark (?) in the following expression (you are not required to calculate the exact value).

$\sqrt[3]{729.14}+{11.01}^3+60.24\%\text{of}449.86=?$

The correct option is 1610.

To find the approximate value that replaces the question mark (?), we can round off the numbers in the given expression to their nearest whole numbers for easier calculation:

1. $\sqrt[3]{729.14}\approx \sqrt[3]{729}$

Since $9^3=729$, we get:

$\sqrt[3]{729}=9$

2. ${11.01}^3\approx {11}^3$

Calculating ${11}^3$:

${11}^3=1331$

3. $60.24\%\text{of}449.86\approx 60\%\text{of}450$

Calculating $60\%$ of $450$:

$\frac{60}{100}\times 450=270$

Now, substitute these approximate values back into the main expression:

$?\approx 9+1331+270$

Adding the numbers together:

$?\approx 1340+270=1610$

Hence, the approximate value that should replace the question mark is 1610.