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The question in the image asks about an underground tank in the shape of a right cone. Let's break down the problem:

### Given Data:
- The cone-shaped tank has a **base diameter of 5.0 m**, so the **radius (r)** is half of the diameter:
  \[
  r = \frac{5.0}{2} = 2.5 \, \text{m}
  \]
- The **height (h)** of the cone is **3.5 m**.
- **1 m³ = 1 kL** (kilolitre).

### Part (a) - Capacity of the tank (in kL):
We need to calculate the volume of the cone. The formula for the volume of a cone is:
\[
V = \frac{1}{3} \pi r^2 h
\]
Substitute the values of **r = 2.5 m** and **h = 3.5 m** into the formula.

### Part (b) - Water in the tank when the water level is 1 m below the top:
If the water level is 1 m below the top, the height of the water is:
\[
\text{Water height} = 3.5 \, \text{m} - 1 \, \text{m} = 2.5 \, \text{m}
\]
Since the tank is a cone, the volume of water will be proportional to the square of the radius at that height. The radius of the water at 2.5 m height will be smaller than the full radius. The new radius can be found using the similarity of triangles (since the cone's shape forms similar triangles):
\[
\frac{\text{New radius}}{\text{Original radius}} = \frac{\text{Water height}}{\text{Total height}} = \frac{2.5}{3.5}
\]
We can now compute the volume of water in the tank using the same volume formula, but with the new radius and height of 2.5 m.

I'll now calculate both parts (a) and (b).### Results:

- **Part (a):** The total capacity of the tank is approximately **22.9 kL** (kilolitres).
- **Part (b):** When the water level is 1 meter below the top, the volume of water in the tank is approximately **8.35 kL**.

Would you like further details or have any other questions?

### Related Questions:
1. What is the formula to calculate the surface area of the cone-shaped tank?
2. How would the volume change if the tank were only filled to half its height?
3. What would the water volume be if the water height was 1.5 m instead of 2.5 m?
4. How would you calculate the slant height of the cone?
5. How does the volume formula change if the shape of the tank were a cylinder?

### Tip:
To solve for volume or surface area in geometric shapes, always ensure units are consistent before plugging into the formula!

An underground tank has the shape of a right cone. The tank collects the water run-off for a three-storey parking garage. The cone has a base diameter of 5.0 m and a height of 3.5 m. 
a) What is the capacity of the tank to the nearest tenth of a kilolitre?
b) How much water is in the tank when the water level is 1 m below the top of the tank?

Solve for the total capacity of an underground right cone-shaped tank with a base diameter of 5.0 m and a height of 3.5 m. Learn how to calculate the volume of water in the tank when the water level is 1 m below the top using geometry and similar triangle principles.

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