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].
