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First, we need to find the radius of the cylinder using the formula:
\[ \text{Volume of a cylinder} = \pi r^2 h \]
Given that the diameter is 8 cm, the radius (r) is half of that, so \( r = 4 \) cm.
Now we can plug in the values to find the height (h):
\[ 176 = \pi \times 4^2 \times h \]
\[ 176 = 16 \pi h \]
\[ h = \frac{176}{16\pi} \]
\[ h \approx 3 \text{ cm} \]
Therefore, the height of the cylinder is approximately 3 cm.