Question

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Part 1
The volume of a cylinder is 1421pi cmcubed. The height of the cylinder is 29 cm. What is the radius of the​ cylinder?

Answer 1

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.