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:

$\boxed{1 \text{ cube is needed to fill the cone.}}$

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.