Question

What is the height of a cylinder with a radius of 7mm and a volume of 441pi (pi = 3.14).

Answer 1

To find the height of a cylinder when the radius and volume are known, 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.

From the problem, we know:
- \( V = 441\pi \)
- \( r = 7 \text{ mm} \)

First, we can substitute the known values into the volume formula:

\[
441\pi = \pi (7^2) h
\]

Calculating \( 7^2 \):

\[
7^2 = 49
\]

Substituting this back into the equation gives:

\[
441\pi = \pi (49) h
\]

To simplify, we can divide both sides of the equation by \( \pi \):

\[
441 = 49h
\]

Now, to solve for \( h \):

\[
h = \frac{441}{49}
\]

Calculating \( \frac{441}{49} \):

\[
h = 9
\]

Thus, the height of the cylinder is:

\[
\boxed{9 \text{ mm}}
\]