Question

find the volume of the cylinder in cubic millimeters round your answer to the nearest hundredth. 8 mm 13 mm

Answer 1

To find the volume \( V \) of a cylinder, you can use the formula:

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

where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

From your question, it seems that you provided two dimensions: 8 mm and 13 mm. It's common to interpret the larger value as the height \( h \) and the smaller value as the diameter. Since the diameter is mentioned, we should calculate the radius by dividing the diameter by 2.

1. Calculate the radius:
\[
\text{Diameter} = 8 \, \text{mm} \implies r = \frac{8}{2} = 4 \, \text{mm}
\]

2. Assign the height:
\[
h = 13 \, \text{mm}
\]

Now plug these values into the volume formula:

\[
V = \pi (4 \, \text{mm})^2 (13 \, \text{mm})
\]

\[
V = \pi (16 \, \text{mm}^2)(13 \, \text{mm}) = 208\pi \, \text{mm}^3
\]

Now, using \( \pi \approx 3.14159 \):

\[
V \approx 208 \times 3.14159 \approx 652.17872 \, \text{mm}^3
\]

Finally, rounding to the nearest hundredth:

\[
V \approx 652.18 \, \text{mm}^3
\]

Thus, the volume of the cylinder is approximately **652.18 cubic millimeters**.