A concrete silo base has a diameter of 17 feet and six inches and a depth of 8 inche’s. how many cubic yards of concrete are needed for the silo base

To determine the cubic yards of concrete needed for the silo base, we need to calculate the volume of a cylinder, as the base has a circular shape.

### Step 1: Convert Dimensions to Feet
1. **Diameter of the base**: 17 feet and 6 inches.  
   - Convert inches to feet: \( 6 \text{ inches} = 0.5 \text{ feet} \).
   - Total diameter in feet: \( 17 + 0.5 = 17.5 \text{ feet} \).
   - Radius (half of the diameter): \( \frac{17.5}{2} = 8.75 \text{ feet} \).

2. **Depth**: 8 inches.  
   - Convert inches to feet: \( 8 \text{ inches} = \frac{8}{12} = \frac{2}{3} = 0.6667 \text{ feet} \).

### Step 2: Calculate Volume in Cubic Feet
The volume \( V \) of a cylinder is given by:
\[
V = \pi r^2 h
\]
where \( r \) is the radius, and \( h \) is the height (or depth) of the cylinder.

1. Substitute the values:
   \[
   V = \pi \times (8.75)^2 \times 0.6667
   \]
2. Calculate \( V \):
   \[
   V \approx 3.1416 \times 76.5625 \times 0.6667 \approx 160.5 \text{ cubic feet}
   \]

### Step 3: Convert Cubic Feet to Cubic Yards
Since 1 cubic yard = 27 cubic feet, we divide the result by 27:
\[
\text{Volume in cubic yards} = \frac{160.5}{27} \approx 5.94 \text{ cubic yards}
\]

### Answer
Approximately **5.94 cubic yards** of concrete are needed for the silo base.

Would you like further details or have any questions?

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**Related Questions:**
1. How would the volume change if the diameter were increased to 20 feet?
2. What is the effect on volume if the base depth were doubled?
3. How would you calculate the surface area of the silo base?
4. How much concrete is needed if the base depth were increased by 2 inches?
5. How can we use a similar method to calculate the volume of a circular pool?

**Tip:** Always convert all measurements to the same unit before starting calculations for better accuracy.

A concrete silo base has a diameter of 17 feet and six inches and a depth of 8 inches. How many cubic yards of concrete are needed for the silo base?

Learn how to calculate the volume of concrete required for a silo base with a diameter of 17 feet 6 inches and a depth of 8 inches. This problem involves using the volume formula for a cylinder and converting cubic feet to cubic yards, making it ideal for Grades 9-10 geometry students.

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