The volume \( V \) of a right circular cylinder can be calculated using the formula:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- and \( \pi \) is approximately 3.14.
Given:
- \( V = 27,355.68 , \text{mm}^3 \)
- \( r = 22 , \text{mm} \)
- \( \pi \approx 3.14 \)
We can rearrange the formula to solve for \( h \):
\[ h = \frac{V}{\pi r^2} \]
First, we need to calculate \( r^2 \):
\[ r^2 = 22^2 = 484 , \text{mm}^2 \]
Now we can calculate the volume formula:
\[ V = \pi r^2 h \implies h = \frac{V}{\pi r^2} = \frac{27,355.68}{3.14 \times 484} \]
Now calculate \( 3.14 \times 484 \):
\[ 3.14 \times 484 = 1,519.76 \]
Now substitute this value back to find \( h \):
\[ h = \frac{27,355.68}{1,519.76} \approx 17.99 \]
Rounding to the nearest whole number gives:
\[ h \approx 18 , \text{mm} \]
Thus, the height of the cylinder is approximately 18 mm.