Answer :

To determine the height of a cylinder given its radius and volume, we can use the formula for the volume of a cylinder:

[tex]\[ V = \pi r^2 h \][/tex]

where [tex]\( V \)[/tex] is the volume, [tex]\( r \)[/tex] is the radius, and [tex]\( h \)[/tex] is the height. We're given the following values:
- [tex]\( V = 628.32 \, \text{cm}^3 \)[/tex]
- [tex]\( r = 5 \, \text{cm} \)[/tex]

We need to solve for [tex]\( h \)[/tex]. Rearrange the formula to isolate [tex]\( h \)[/tex]:

[tex]\[ h = \frac{V}{\pi r^2} \][/tex]

Substitute the given values into the equation:

[tex]\[ h = \frac{628.32}{\pi \cdot (5)^2} \][/tex]

Calculate the denominator first:

[tex]\[ 5^2 = 25 \][/tex]
[tex]\[ \pi \cdot 25 \approx 3.14159 \cdot 25 \approx 78.53975 \][/tex]

Now, divide the volume by this product:

[tex]\[ h = \frac{628.32}{78.53975} \approx 8.000018707479974 \][/tex]

Therefore, the height of the cylinder is approximately 8.000018707479974 cm.

To determine the height to the nearest centimeter, we round this value:

[tex]\[ \text{Height} \approx 8 \, \text{cm} \][/tex]

Thus, the height of the cylinder, correct to the nearest centimeter, is [tex]\( 8 \, \text{cm} \)[/tex].