https://file.aiquickdraw.com/mathbot/file/1727062526199hgtcpofq.jpg

To find the volume of the cylinder shown in the image, we use the formula for the volume of a cylinder:

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

Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height of the cylinder.

From the image:
- The radius \( r = 8 \) inches.
- The height \( h = 10 \) inches.

Now we calculate the exact volume in terms of \( \pi \):

\[
V = \pi (8)^2 (10) = \pi \times 64 \times 10 = 640\pi \, \text{cubic inches}.
\]

For the approximate volume:
\[
V \approx 640 \times 3.1416 = 2010.62 \, \text{cubic inches}.
\]

Rounded to the nearest whole number:
\[
V \approx 2011 \, \text{cubic inches}.
\]

### Summary:
- **Exact Volume:** \( 640\pi \, \text{cubic inches} \)
- **Approximate Volume:** \( 2011 \, \text{cubic inches} \)

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you calculate the surface area of a cylinder?
2. What happens to the volume if the radius is doubled?
3. How would you compute the volume if the cylinder were a hollow pipe?
4. How is the formula for the volume of a cylinder derived?
5. Can the formula for the volume of a cylinder be applied to cones or other shapes?

**Tip:** Always ensure that units for radius and height are in the same measurement system when calculating volumes.

Find the volume of the figure. Express the answer in terms of π and then round to the nearest whole number.

Learn how to find the volume of a cylinder with a radius of 8 inches and a height of 10 inches. This guide walks you through the process of calculating the exact volume in terms of π and rounding it to the nearest whole number. Perfect for students in Grades 8-10.

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