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 of the cylinder,
- \( r \) is the radius, and
- \( h \) is the height.
Given:
- \( V = 27355.68 , \text{mm}^3 \)
- \( r = 22 , \text{mm} \)
- \( \pi \approx 3.14 \)
Plugging the values into the formula, we have:
\[ 27355.68 = 3.14 \times (22^2) \times h \]
First, calculate \( 22^2 \):
\[ 22^2 = 484 \]
Now substitute this value back into the equation:
\[ 27355.68 = 3.14 \times 484 \times h \]
Next, calculate \( 3.14 \times 484 \):
\[ 3.14 \times 484 = 1518.56 \]
Now the equation becomes:
\[ 27355.68 = 1518.56 \times h \]
To find \( h \), divide both sides by 1518.56:
\[ h = \frac{27355.68}{1518.56} \]
Calculating this gives:
\[ h \approx 18 \]
Thus, the height of the cylinder is approximately:
\[ \boxed{18 , \text{mm}} \]