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

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

Given:

• Volume, $V = 753.3 \, \text{dm}^3 = 753.3 \times 1000 \, \text{cm}^3 = 753300 \, \text{cm}^3$ (since $1 \, \text{dm}^3 = 1000 \, \text{cm}^3$)
• Radius, $r = 8.4 \, \text{cm}$

Substituting into the volume formula:

$753300 = \frac{1}{3} \pi (8.4)^2 h$

Now, let's solve for $h$.The height of the cone is approximately $10194.85 \, \text{cm}$.

Would you like more details on this calculation or have any other questions?

Here are 5 related questions:

1. How do you convert between different volume units like dm³ to cm³?
2. What is the relationship between the height and slant height of a cone?
3. How would the volume change if the radius was doubled?
4. Can you find the surface area of this cone with the given dimensions?
5. How does the formula for the volume of a cone compare to that of a cylinder?

Tip: Always ensure consistent units when solving geometry problems involving volume or area.