Question

The circumference of a redwood tree trunk is 16π ft, and it is 100 ft tall. Using a right cylinder to model the trunk, what is the approximate volume of the redwood tree trunk?

2,560π ft3
640π ft3
25,600π ft3
6,400π ft3

Answer 1

To find the volume of the redwood tree trunk modeled as a right cylinder, we can use the formula for the volume \( V \) of a cylinder:

\[
V = \pi r^2 h
\]

where \( r \) is the radius of the base of the cylinder and \( h \) is the height.

### Step 1: Find the radius from the circumference
The circumference \( C \) of a circle is given by the formula:

\[
C = 2\pi r
\]

Given that the circumference of the trunk is \( 16\pi \) ft, we can set up the equation:

\[
2\pi r = 16\pi
\]

To find \( r \), divide both sides by \( 2\pi \):

\[
r = \frac{16\pi}{2\pi} = 8 \text{ ft}
\]

### Step 2: Use the height
The height \( h \) of the trunk is given as \( 100 \) ft.

### Step 3: Calculate the volume
Now that we have \( r = 8 \) ft and \( h = 100 \) ft, we can plug these values into the volume formula:

\[
V = \pi r^2 h = \pi (8)^2 (100)
\]

Calculating \( r^2 \):

\[
8^2 = 64
\]

Now substitute back into the volume formula:

\[
V = \pi (64)(100) = 6400\pi \, \text{ft}^3
\]

### Conclusion
The approximate volume of the redwood tree trunk is:

\[
\boxed{6400\pi \, \text{ft}^3}
\]