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The problem asks to find the volume \( V \) of a propane tank, which consists of a right circular cylinder with two hemispheres welded at the ends. The function should be expressed in terms of \( r \), the radius of the cylinder and hemispheres, and \( l \), the length of the cylinder.

The volume of this composite object is the sum of the volume of the cylindrical part and the two hemispheres.

### Step-by-step breakdown:

1. **Volume of the cylindrical part:**
   The volume of a cylinder is given by:
   \[
   V_{\text{cylinder}} = \pi r^2 l
   \]
   where \( r \) is the radius and \( l \) is the length of the cylinder.

2. **Volume of the hemispheres:**
   The volume of a sphere is:
   \[
   V_{\text{sphere}} = \frac{4}{3} \pi r^3
   \]
   Since there are two hemispheres, which together form one full sphere, the total volume of the two hemispheres is:
   \[
   V_{\text{hemispheres}} = \frac{4}{3} \pi r^3
   \]

3. **Total volume of the propane tank:**
   The total volume \( V \) is the sum of the volume of the cylinder and the volume of the two hemispheres:
   \[
   V = V_{\text{cylinder}} + V_{\text{hemispheres}} = \pi r^2 l + \frac{4}{3} \pi r^3
   \]

Therefore, the volume of the propane tank as a function of \( r \) and \( l \) is:
\[
V = \pi r^2 l + \frac{4}{3} \pi r^3
\]

Let me know if you'd like further clarification or additional details.

Here are 5 related questions you can explore:
1. How would the volume formula change if the cylinder had a different shape for its ends?
2. What is the surface area of the tank in terms of \( r \) and \( l \)?
3. How does the volume change as the radius \( r \) increases but the cylinder length \( l \) stays constant?
4. Can you express the total volume as a single factor of \( \pi \)?
5. What is the ratio of the volume of the hemispheres to the volume of the cylinder?

**Tip**: When solving composite volume problems, break down the shape into simpler components like spheres, cylinders, and cones to make the calculation easier.

A propane tank is constructed by welding hemispheres to the ends of a right circular cylinder. Write the volume V of the tank as a function of r and l, where r is the radius of the cylinder and hemispheres, and l is the length of the cylinder.

Learn how to calculate the volume of a propane tank that consists of a right circular cylinder with hemispherical ends. This problem involves geometry concepts like volume calculation for composite shapes, using formulas for cylinders and spheres. Suitable for high school students in Grades 9-12.

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