To calculate the volume of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
- Find the radius: The diameter of the cone is 22 mm, so the radius \( r \) is:
\[ r = \frac{22}{2} = 11 \text{ mm} \]
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Use the height: The height \( h \) of the cone is given as 19 mm.
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Plug in the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (11)^2 \times 19 \]
- Calculate \( (11)^2 \):
\[ (11)^2 = 121 \]
- Now substitute that into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 121 \times 19 \]
- Calculating \( 121 \times 19 \):
\[ 121 \times 19 = 2299 \]
- Now substitute back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 2299 \]
- Calculate \( 3.14 \times 2299 \):
\[ 3.14 \times 2299 = 7210.86 \]
- Now divide by 3:
\[ V = \frac{7210.86}{3} \approx 2403.62 \]
Thus, the volume of the cone is approximately
\[ \boxed{2403.62 \text{ mm}^3} \]
rounded to the nearest hundredth.