To find the height of the cone, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
Where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height.
We are given:
- Volume \( V = 376.8 \) cubic millimeters,
- \( \pi \approx 3.14 \).
We also need to note that from the problem you provided, it seems like the radius is not mentioned. However, if you assume a radius (for example, given as 6 mm, or if that's assumed), you can then solve for the height. I'll proceed with using \( r = 6 \) mm.
First, let's plug in the values into the formula:
\[ 376.8 = \frac{1}{3} \times 3.14 \times (6)^2 \times h \]
Calculating \( 6^2 \):
\[ 6^2 = 36 \]
Now substitute this into the volume formula:
\[ 376.8 = \frac{1}{3} \times 3.14 \times 36 \times h \]
Calculating \( \frac{1}{3} \times 3.14 \times 36 \):
\[ \frac{1}{3} \times 3.14 \times 36 = \frac{113.04}{3} = 37.68 \]
Now the equation becomes:
\[ 376.8 = 37.68h \]
To solve for \( h \), divide both sides by \( 37.68 \):
\[ h = \frac{376.8}{37.68} \approx 10 \]
Rounded to the nearest hundredth, the height \( h \) is:
\[ h \approx 10.00 \text{ mm} \]
Thus, the height of the cone is approximately 10.00 millimeters. If the radius was something other than 6 mm, please provide that information for accurate calculations.
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