https://file.aiquickdraw.com/mathbot/file/1729561494347uew7o7s3.jpg

The image provided shows a lesson on "Volume Measurement – Cylinders," which involves calculating the volume of a cylindrical shape using the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \approx 3.1416 \).

### Example from the Image:
The problem involves finding the volume of a cylinder with a radius of 12 feet and a height of 30 feet:

\[
V = 3.1416 \times 12^2 \times 30
\]

\[
V = 3.1416 \times 144 \times 30 = 13,574.56 \, \text{cubic feet}.
\]

### Review Problems:
There are two review problems listed in the image:

1. **Problem 1:**
   A cross-section of a cylindrical cistern is shown. The problem asks for the volume of the cistern. It appears to be 4 feet in radius and 4 feet in height based on the provided diagram, so you would use the same formula:

   \[
   V = \pi r^2 h
   \]
   where \( r = 4' \) and \( h = 4' \).

2. **Problem 2:**
   It asks how many cubic yards of earth are excavated for a concrete cistern with a diameter of 9 feet 6 inches and a depth of 10 feet 0 inches. An allowance of 18 inches is made for form work, and the top of the cistern is 4 feet below grade. The diameter is given, so you can use the formula to find the volume by first finding the radius from the diameter and subtracting allowances.

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Would you like me to calculate one of these problems in more detail or clarify any part of the example? 

### 5 Related Questions:
1. How do you convert between cubic feet and cubic yards when measuring volume?
2. How does adding an allowance for form work affect the calculation of volume?
3. How would the volume formula change if we had a hollow cylinder instead of a solid one?
4. What are the real-world applications of calculating the volume of a cylinder?
5. Can this formula be applied to irregularly shaped cylinders, such as truncated cylinders?

### Tip:
Always ensure all dimensions are in the same units (feet, inches, etc.) before calculating the volume to avoid errors.

Find the volume of a circular cylinder with a radius of 12 feet and a height of 30 feet. Additionally, calculate the volume of a cylindrical cistern and the amount of cubic yards of earth excavated for another cistern with given dimensions.

Learn how to calculate the volume of cylinders, including cisterns, using the formula V = πr^2h. Explore real-world applications such as determining the volume of a cylindrical cistern and the amount of earth excavated for a concrete cistern. Suitable for high school students.

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