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Let's tackle each question in the "Review Problems" section step-by-step.

### Problem 1:
We are given:
- **Diameter** of the cistern = 4'0" (or 4 feet)
- Therefore, the **radius** \( r = \frac{4}{2} = 2 \) feet.
  
Using the volume formula for a cylinder:
\[
V = \pi r^2 h
\]
Substitute the values:
- **Radius** \( r = 2 \) feet
- **Height** \( h = 8 \) feet

Using \( \pi = 3.1416 \):
\[
V = 3.1416 \times 2^2 \times 8
\]
\[
V = 3.1416 \times 4 \times 8
\]
\[
V = 3.1416 \times 32
\]
\[
V \approx 100.53 \text{ cubic feet}
\]

So, the volume of the cistern is approximately **100.53 cubic feet**.

---

### Problem 2:
For this problem:
- **Outside diameter** = 9'6" = 9.5 feet
- **Outside depth** = 10'0" = 10 feet
- Allowance for form work (walls) is 18 inches (1.5 feet), meaning we’ll reduce 1.5 feet from the diameter and depth for the actual inside measurements.

#### Step 1: Find the effective inner diameter and height.
- **Effective inner diameter** = 9.5 - 2(1.5) = 6.5 feet
  - **Radius** \( r = \frac{6.5}{2} = 3.25 \) feet
- **Effective inner depth (height)** = 10 - 1.5 = 8.5 feet

#### Step 2: Calculate the volume.
Using the formula:
\[
V = \pi r^2 h
\]
where:
- \( \pi = 3.1416 \)
- \( r = 3.25 \)
- \( h = 8.5 \)

\[
V = 3.1416 \times (3.25)^2 \times 8.5
\]
\[
V = 3.1416 \times 10.5625 \times 8.5
\]
\[
V \approx 282.74 \text{ cubic feet}
\]

#### Step 3: Convert to cubic yards.
Since there are 27 cubic feet in a cubic yard:
\[
\frac{282.74}{27} \approx 10.47 \text{ cubic yards}
\]

So, the amount of earth to be excavated is approximately **10.47 cubic yards**.

---

Would you like a deeper breakdown of these calculations or have any specific questions? 

### Related Questions:
1. How would you calculate the volume of a cylinder if the radius and height were given in different units (e.g., inches and feet)?
2. If the cistern in Problem 1 had an irregular cross-section, how would the volume formula change?
3. How does the volume calculation change if you need to account for a slanted top or bottom in a cylinder?
4. What is the impact of using different approximations for \( \pi \) on the volume results?
5. How would adding a hemispherical dome on top of the cistern affect the total volume?

**Tip:** Always ensure units are consistent throughout the calculation to avoid conversion errors.

Solve the following questions:
1. A cross section of a cylindrical cistern is shown. What is the volume of the cistern?
2. How many cubic yards of earth are excavated for a concrete cistern with an outside diameter of 9'6" and a depth of 10'0", with an 18-inch allowance for form work?

Calculate the volume of a cylindrical cistern and determine the amount of earth to be excavated for a concrete cistern with specific dimensions. This solution includes step-by-step volume calculations and unit conversions, suitable for students in Grades 8-10.

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