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To find the volume of the propane tank, which is a combination of a cylinder with hemispheres at both ends, we need to calculate the volumes of both parts separately and then add them together.

### Given Information:
- **Diameter of the cylinder (and hemispheres):** 6.50 ft (this implies the radius \( r = \frac{6.50}{2} = 3.25 \) ft).
- **Length of the cylindrical part:** 4.00 ft.

### Step 1: Volume of the cylindrical part
The volume \( V_{\text{cylinder}} \) of a cylinder is given by the formula:

\[
V_{\text{cylinder}} = \pi r^2 h
\]

Where:
- \( r = 3.25 \) ft is the radius of the cylinder.
- \( h = 4.00 \) ft is the height (or length) of the cylinder.

### Step 2: Volume of the hemispherical ends
Each hemisphere has a volume \( V_{\text{hemisphere}} \) which is half the volume of a sphere. The volume of a sphere is:

\[
V_{\text{sphere}} = \frac{4}{3} \pi r^3
\]

Thus, the volume of one hemisphere is:

\[
V_{\text{hemisphere}} = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3
\]

Since there are two hemispheres, the total volume of both hemispheres is:

\[
V_{\text{total hemispheres}} = 2 \times \frac{2}{3} \pi r^3 = \frac{4}{3} \pi r^3
\]

### Step 3: Total Volume of the tank
The total volume \( V_{\text{total}} \) of the tank is the sum of the volume of the cylinder and the volume of the two hemispheres:

\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{total hemispheres}}
\]

Let me compute this now.The total volume of the propane tank is approximately **276.53 cubic feet**.

Would you like further details or have any questions?

Here are five related questions that might interest you:
1. How would the volume change if the radius was doubled?
2. What would be the surface area of the propane tank?
3. How can we calculate the weight of the propane if we know its density?
4. How does the volume formula for a cylinder differ from that of a prism?
5. What real-life applications can involve calculating volumes of composite shapes?

**Tip:** When dealing with composite shapes, always break the shape into simpler geometric components (like cylinders and hemispheres) to simplify the volume calculation.

A propane tank has the shape of a cylinder with a hemisphere at each end. The diameter is 6.50 ft and the length of the cylindrical part is 4.00 ft. Find the volume of the tank.

Find the volume of a propane tank that has a cylindrical body with hemispherical ends. The diameter is 6.50 ft and the cylinder length is 4.00 ft. Learn how to apply volume formulas for cylinders and hemispheres to solve composite shape problems.

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