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 of the base, and \( h \) is the height of the cone.
Given:
- Diameter = 22 mm, so the radius \( r = \frac{22}{2} = 11 \) mm
- Height \( h = 19 \) mm
Now, substitute the values into the formula:
\[ V = \frac{1}{3} \pi (11)^2 (19) \] \[ V = \frac{1}{3} \pi (121) (19) \] \[ V = \frac{1}{3} \pi (2299) \] \[ V \approx \frac{1}{3} \times 3.14159 \times 2299 \] \[ V \approx \frac{1}{3} \times 7227.42359 \] \[ V \approx 2419.14119 \text{ mm}^3 \] \[ V \approx 2419.14 \text{ mm}^3 \]
Rounding to the nearest hundredth, the volume of the cone is approximately 2419.14 mm³.