https://file.aiquickdraw.com/mathbot/file/1727407697112d006r5wc.jpg

Let's break down the problem from the image to find the total volume of the tank.

### Problem details:
- The tank consists of a **cylindrical part** and a **hemispherical top**.
- The **diameter** of the tank is given as **8000 mm**, which is **8 meters** (since 1000 mm = 1 m).
- The **overall height** of the tank is **16 meters**.

To find the total volume of the tank, we need to compute:
1. The volume of the **cylinder**.
2. The volume of the **hemisphere**.

### Step 1: Volume of the cylindrical part
Let the **radius** of the cylinder be \( r = \frac{8}{2} = 4 \, \text{m} \).

The height of the cylindrical part is the overall height minus the height of the hemispherical top. The height of the hemisphere is equal to its radius, so the height of the cylindrical part is:
\[
\text{Height of the cylinder} = 16 - 4 = 12 \, \text{m}
\]

The volume \( V_{\text{cylinder}} \) of the cylinder is given by:
\[
V_{\text{cylinder}} = \pi r^2 h = \pi (4^2) (12) = \pi \times 16 \times 12 = 192\pi \, \text{m}^3
\]
\[
V_{\text{cylinder}} \approx 603.19 \, \text{m}^3
\]

### Step 2: Volume of the hemispherical top
The volume \( V_{\text{hemisphere}} \) of a hemisphere is given by:
\[
V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 = \frac{2}{3} \pi (4^3) = \frac{2}{3} \pi \times 64 = \frac{128}{3} \pi \, \text{m}^3
\]
\[
V_{\text{hemisphere}} \approx 134.04 \, \text{m}^3
\]

### Step 3: Total Volume of the tank
Now, adding the volumes of the cylinder and hemisphere, we get the total volume of the tank:
\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{hemisphere}} = 603.19 + 134.04 \approx 737.23 \, \text{m}^3
\]

### Conclusion:
The total volume of the tank is approximately **737.23 cubic meters**, which corresponds to option **c) 737.225 m³**.

---

Do you have any questions or need further clarification?

Here are five related questions you might find useful:
1. How do you calculate the volume of a cone or sphere in a tank problem?
2. How would the total volume change if the diameter of the tank increased?
3. What happens to the volume of the cylinder if the radius doubles but the height stays the same?
4. How would the calculation change if the tank had a conical top instead of a hemispherical one?
5. Why is the volume of a hemisphere half of the volume of a full sphere?

**Tip**: Always check units carefully when solving volume problems, especially when dimensions are provided in different unit systems!

A cylindrical tank with a hemispherical top has a diameter of 8000 mm and an overall height of 16 m. Find the total volume of the tank in cubic meters.

Learn how to calculate the total volume of a cylindrical tank with a hemispherical top. This problem covers essential geometry concepts, such as the volume formulas for cylinders and hemispheres, and provides a step-by-step solution. Suitable for Grades 10-12.

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