To determine the square footage of the wall surface on the inside of the silo, let's go through the calculations step-by-step.

Step 1: Understanding the Shape and Dimensions

The silo is a cylinder, with:

• Volume $V = 3,392.7 \, \text{cubic feet}$
• Height $h = 30 \, \text{feet}$

Step 2: Formula for the Volume of a Cylinder

The volume of a cylinder is given by: $V = \pi r^2 h$ where:

• $V$ is the volume,
• $r$ is the radius, and
• $h$ is the height.

Step 3: Solve for the Radius $r$

Rearrange the formula to solve for $r$: $r^2 = \frac{V}{\pi h}$ Substitute the given values: $r^2 = \frac{3,392.7}{\pi \times 30}$ $r^2 = \frac{3,392.7}{94.2478} \approx 36$ $r \approx \sqrt{36} = 6 \, \text{feet}$

Step 4: Calculate the Wall Surface Area (Lateral Surface Area)

The formula for the lateral surface area of a cylinder (the wall surface inside the silo) is: $A = 2 \pi r h$ Substitute $r = 6$ feet and $h = 30$ feet: $A = 2 \pi \times 6 \times 30$ $A = 360 \pi$ $A \approx 1,130.97 \, \text{square feet}$

Final Answer

The inside wall surface area of the silo is approximately 1,130.97 square feet.

Would you like more details, or do you have any questions?

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Here are 5 related questions to deepen your understanding:

1. How would the wall surface area change if the height of the silo were doubled?
2. What would be the volume of a silo with the same radius but a different height?
3. How does the volume formula for a cylinder compare to that of a sphere?
4. If the silo had a roof, what would be the total surface area (including top and bottom)?
5. How do different values of radius and height affect the volume of a cylinder?

Tip: For cylinders, the wall area is directly proportional to both the radius and the height, so any increase in these measurements will increase the surface area.