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

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

Given:

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

Now, we can solve for $h$:

$566.77 = \frac{1}{3} \pi (9.5)^2 h$

Simplifying the equation:

$566.77 = \frac{1}{3} \pi (90.25) h$

$566.77 = \frac{1}{3} \times 3.1416 \times 90.25 \times h$

Now solve for $h$:

$566.77 = 94.67 h$

$h = \frac{566.77}{94.67} \approx 5.997 \, \text{m}$

Thus, the height $h$ is approximately $5.997 \, \text{m}$.

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Would you like further details or have any questions?

Here are 5 related questions:

1. How would the volume change if the radius were doubled?
2. What is the surface area of this cone, including the base?
3. How does the volume of a cone compare to a cylinder with the same height and radius?
4. Can you derive the formula for the lateral surface area