We are given the formula for the volume of a cone:

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

Where:

• $V$ is the volume of the cone,
• $r$ is the radius,
• $h$ is the height.

From the problem:

• $V = 800 \, \text{cm}^3$,
• $r = 7 \, \text{cm}$.

We need to find $h$.

Step 1: Rearrange the formula to solve for $h$:

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

Step 2: Substitute the known values:

$h = \frac{3 \cdot 800}{\pi \cdot (7)^2}$

Step 3: Simplify:

$h = \frac{2400}{\pi \cdot 49}$ h = \frac{2400}{153.93804} \quad (\text{approximate \pi = 3.14159}) $h \approx 15.6 \, \text{cm}$

Final Answer:

The height of the cone is approximately 15.6 cm (to 1 decimal place).

Would you like a detailed explanation of the steps?
Here are some additional questions for further exploration:

1. How does changing the radius affect the height for the same volume?
2. Can we derive the formula for the surface area of a cone from its geometry?
3. How would the calculation change if the volume was given in liters?
4. How is the formula for the volume of a cone derived geometrically?
5. What is the relationship between a cone and a cylinder with the same base and height?

Tip: Always check the units to ensure they are consistent when solving problems involving volume and dimensions.