Question

A)You are examining a log that you find on the ground. The diameter of the log is 32 inches, but the length of the log is unknown. Find the log’s length if its volume is 10,000π in.3. Round your answer to the nearest hundredth.(1 point)
length=$$ in.

Answer 1

To find the length of the log, 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 (or length) of the cylinder.

1. **Determine the radius**: The diameter of the log is given as 32 inches, so the radius \( r \) is half of that:

\[
r = \frac{32}{2} = 16 \text{ inches}
\]

2. **Set up the equation**: Given that the volume \( V = 10,000\pi \) cubic inches, we can substitute the known values into the volume formula:

\[
10,000\pi = \pi (16^2) h
\]

3. **Simplify the equation**: First, we simplify \( 16^2 \):

\[
16^2 = 256
\]

Now replacing in the equation gives us:

\[
10,000\pi = \pi (256) h
\]

4. **Cancel \( \pi \) from both sides**:

\[
10,000 = 256h
\]

5. **Solve for \( h \)**:

\[
h = \frac{10,000}{256}
\]

Calculating \( h \):

\[
h = 39.0625 \text{ inches}
\]

6. **Round to the nearest hundredth**:

The length of the log is

\[
h \approx 39.06 \text{ inches}
\]

Thus, the length of the log is

\[
\boxed{39.06} \text{ in.}
\]