what is the volume of this cone? diameter 22 mm height 19 mm

1 answer

To find 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 of the cone.

  1. Find the radius: The radius \( r \) is half of the diameter. Given a diameter of 22 mm, the radius is:

\[ r = \frac{22 \text{ mm}}{2} = 11 \text{ mm} \]

  1. Height: The height \( h \) is given as 19 mm.

  2. Now plug in the values:

\[ V = \frac{1}{3} \pi (11 \text{ mm})^2 (19 \text{ mm}) \] \[ = \frac{1}{3} \pi (121 \text{ mm}^2) (19 \text{ mm}) \] \[ = \frac{1}{3} \pi (2299 \text{ mm}^3) \] \[ = \frac{2299}{3} \pi \text{ mm}^3 \] \[ \approx 766.33 \pi \text{ mm}^3 \] \[ \approx 2417.6 \text{ mm}^3 \quad (\text{using } \pi \approx 3.14159) \]

Thus, the volume of the cone is approximately 2417.6 mm³.