What is the volume of a cylinder with a height of 7.1 ft and a base with a diameter of 12.8 ft, to the nearest tenth of a cubic foot?

To find the volume of a cylinder, we use the formula:

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

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

### Step 1: Find the radius of the base
The diameter of the base is given as 12.8 ft. The radius is half of the diameter:

\[
r = \frac{12.8}{2} = 6.4 \text{ ft}
\]

### Step 2: Apply the formula
Now substitute the radius \( r = 6.4 \) ft and the height \( h = 7.1 \) ft into the volume formula:

\[
V = \pi (6.4)^2 (7.1)
\]

\[
V = \pi (40.96)(7.1)
\]

\[
V \approx 3.1416 \times 290.816
\]

\[
V \approx 914.7 \text{ cubic feet}
\]

So, the volume of the cylinder is approximately **914.7 cubic feet**.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. How does the volume of a cylinder change if the radius is doubled?
2. What is the formula for the surface area of a cylinder?
3. How would the volume of the cylinder change if the height was halved?
4. Can the volume formula for a cylinder be applied to other 3D shapes?
5. What real-life objects can be modeled as cylinders?

**Tip:** Remember, the radius is always half of the diameter when dealing with circles or cylindrical shapes!

Learn how to calculate the volume of a cylinder with a diameter of 12.8 ft and height of 7.1 ft. This problem demonstrates the use of the formula V = πr²h and provides step-by-step calculations. Ideal for students in Grades 8-10.

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