Question 4

Explanation

Identifying Geometric Relationships

It is given that the radius ($r$) of the package is half of its height ($t$), so we can write $r = \frac{1}{2}t$. The volume of the cylindrical package is given as $V = \frac{729\pi}{4} \text{ cm}^3$.

Calculating the Height

Using the cylinder volume formula, we substitute the value of $r$ to solve for $t$.

Thus, the height of the package is $9 \text{ cm}$.