To find the radius of a 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, and
- \( h \) is the height.
We are given:
- \( V = 1421\pi \) cm³
- \( h = 29 \) cm
We can plug in the values into the volume formula:
\[ 1421\pi = \pi r^2 (29) \]
First, we'll divide both sides by \( \pi \):
\[ 1421 = r^2 \cdot 29 \]
Now, divide both sides by 29 to solve for \( r^2 \):
\[ r^2 = \frac{1421}{29} \]
Calculating the right side:
\[ r^2 = 49 \]
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{49} = 7 \]
Therefore, the radius of the cylinder is \( \boxed{7} \) cm.
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