Question

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 in this case).

Given:
- The diameter of the log is 32 inches, so the radius \( r \) is half of the diameter:

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

- The volume \( V \) is given as \( 10,000\pi \) cubic inches.

Now we can substitute the values into the volume formula and solve for \( h \):

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

We can cancel \( \pi \) from both sides (assuming \( \pi \) is not zero):

\[
10,000 = 16^2 h
\]

Calculating \( 16^2 \):

\[
16^2 = 256
\]

Now we substitute this back into the equation:

\[
10,000 = 256h
\]

To solve for \( h \):

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

Calculating \( \frac{10,000}{256} \):

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

Rounded to the nearest hundredth, the length of the log is:

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