To find the missing height $h$ of the cone, we can use the formula for the volume of a cone:

$V = \frac{1}{3} \pi r^2 h$

Given:

• Volume $V = 566.77 \, \text{m}^3$
• Radius $r = 9.5 \, \text{m}$

We can rearrange the formula to solve for $h$:

$h = \frac{3V}{\pi r^2}$

Substituting the known values:

$h = \frac{3 \times 566.77}{\pi \times (9.5)^2}$

Now, let's calculate that.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can calculate the height manually by following the steps below:

$h = \frac{3 \times 566.77}{\pi \times (9.5)^2}$

1. Square the radius: $9.5^2 = 90.25$
2. Multiply by $\pi$ (approximately $3.1416$): $90.25 \times \pi = 283.53$
3. Multiply the volume by 3: $566.77 \times 3 = 1700.31$
4. Finally, divide the result by $283.53$ to get the height.

Would you like more details or have any questions?

Here are five related questions to deepen your understanding:

1. How does the volume formula for a cone compare to that of a cylinder?
2. What happens to the volume if the radius is doubled?
3. How can you find the radius if the height and volume are given?
4. What are the units of each variable in the volume formula?
5. How does the cone’s volume change if only the height increases?

Tip: Always check that your units are consistent when calculating physical dimensions.