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To solve this problem, we need to complete two main steps:

1. **Calculate the weight of the cylindrical solid.**
2. **Determine the load on each leg of the double-basket hitch.**

Here's a breakdown of the process:

### Step 1: Calculate the Weight of the Cylindrical Solid
The volume \( V \) of a cylinder is given by:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the cylinder, and
- \( h \) is the height (or length) of the cylinder.

From the diagram:
- The diameter of the cylinder is \( 2 \, \text{ft} \), so the radius \( r = 1 \, \text{ft} \).
- The height (or length) of the cylinder \( h = 17 \, \text{ft} \).

Thus, the volume of the cylinder is:
\[
V = 3.14 \times (1)^2 \times 17 = 3.14 \times 17 = 53.38 \, \text{cubic feet}
\]

Given the density of the cylindrical solid is \( 547 \, \text{lbs/ft}^3 \), the weight \( W \) of the cylinder is:
\[
W = \text{density} \times \text{volume} = 547 \times 53.38 \approx 29200 \, \text{lbs}
\]

### Step 2: Calculate the Load on Each Leg of the Double-Basket Hitch
For a double-basket hitch setup, the load on each leg depends on the angle of the sling. Using trigonometry:
- Each sling length is \( 16.4 \, \text{ft} \),
- The distance between the sling connections at the top and bottom is \( 14 \, \text{ft} \).

Using these values, we can calculate the load on each leg with the formula:
\[
\text{Load per leg} = \frac{W}{2 \cos(\theta)}
\]
where \( \cos(\theta) = \frac{\text{vertical separation}}{\text{sling length}} = \frac{14}{16.4} \). 

Calculating \( \theta \) and then the load per leg, let me work it out.The calculations yield the following:

1. **Weight of the cylindrical solid**: Approximately \( 29,199 \) lbs (rounded to the nearest lb).
2. **Load on each leg of the double-basket hitch**: Approximately \( 17,102.2 \) lbs (rounded to the nearest tenth of a lb).

Would you like further details or have any questions?

Here are some related questions that might help deepen your understanding:
1. How would the weight change if the density of the material were different?
2. How would a change in the sling length affect the load on each leg?
3. What effect would increasing the diameter of the cylinder have on its weight?
4. Why is the angle of the sling important in calculating the load per leg?
5. How would the result differ if this were a single-basket hitch?

**Tip:** Always check that units are consistent in engineering problems to avoid errors in calculations.

Calculate the weight of the cylindrical solid and the load on each leg of the double-basket hitch. The cylindrical solid has a density of 547 lbs/cu. ft. and dimensions of 2 ft diameter and 17 ft length.

Learn how to calculate the weight of a cylindrical solid with a density of 547 lbs/cu. ft. and determine the load on each leg of a double-basket hitch. The problem involves geometry, trigonometry, and static load distribution with key concepts explained step-by-step.

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