To find the height of a right circular cylinder, we can use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
Where:
- \(V\) is the volume,
- \(r\) is the radius,
- \(h\) is the height, and
- \(\pi\) is approximately 3.14.
Given:
- \(V = 27,355.68 , \text{mm}^3\)
- \(r = 22 , \text{mm}\)
- \(\pi = 3.14\)
We need to find the height \(h\). Rearranging the formula to solve for \(h\):
\[ h = \frac{V}{\pi r^2} \]
Now we will calculate \(r^2\):
\[ r^2 = 22^2 = 484 , \text{mm}^2 \]
Next, plug in the values:
\[ h = \frac{27355.68}{3.14 \times 484} \]
Calculating \(3.14 \times 484\):
\[ 3.14 \times 484 = 1519.76 \]
Now substitute this back into the equation for \(h\):
\[ h = \frac{27355.68}{1519.76} \approx 17.98 , \text{mm} \]
Thus, the height of the cylinder is approximately 17.98 mm.