https://file.aiquickdraw.com/mathbot/file/1736094801205n6oltj7e.jpg

To solve question 6 from the image, let us break it down step by step.

---

### Problem:

- A cone has a **radius of 6 cm** and a **height of 6 cm**.  
- A cube has an **edge length of 6 cm**.  
- We need to find how many times the cube needs to be emptied to fill the cone completely with water.  

---

### Step 1: Volume of the cone  
The formula for the volume of a cone is:  
\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]  
Where:  
- \(r = 6 \, \text{cm}\) (radius)  
- \(h = 6 \, \text{cm}\) (height)  
- \(\pi = 3\) (as stated in the question)  

Substitute the values:
\[
V_{\text{cone}} = \frac{1}{3} \times 3 \times 6^2 \times 6
\]
\[
V_{\text{cone}} = \frac{1}{3} \times 3 \times 36 \times 6
\]
\[
V_{\text{cone}} = 36 \times 6 = 216 \, \text{cm}^3
\]

So, the **volume of the cone** is:
\[
216 \, \text{cm}^3
\]

---

### Step 2: Volume of the cube  
The formula for the volume of a cube is:  
\[
V_{\text{cube}} = a^3
\]  
Where \(a = 6 \, \text{cm}\) (edge length).  

Substitute the value:
\[
V_{\text{cube}} = 6^3 = 216 \, \text{cm}^3
\]

So, the **volume of the cube** is:
\[
216 \, \text{cm}^3
\]

---

### Step 3: Calculate how many cubes are needed to fill the cone  
The volume of the cone and the cube are equal (\(216 \, \text{cm}^3\)). This means **1 cube** is enough to completely fill the cone.

---

### Final Answer:
\[
\boxed{1 \text{ cube is needed to fill the cone.}}
\]

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Would you like further clarification or a detailed explanation of the concepts? Here are 5 related questions:

1. How is the volume formula for a cone derived?
2. How does the cube's edge length relate to its volume?
3. What happens if the cone's height or radius changes?
4. Why is \(\pi = 3\) used instead of the more accurate value?
5. Can you calculate the total surface area of the cube and cone?

---

### Tip:
Always compare the units of volume carefully when working with different shapes to ensure consistency.

How many times do we need to fill the cube in order to fill the cone completely with water? (Use π = 3.)

Explore how to calculate the volume of a cone and a cube with equal dimensions and determine how many times the cube's volume can fill the cone. This problem uses key geometric formulas and assumes π = 3, making it suitable for Grades 6-8 students.

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