Question

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

Answer 1

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:

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

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

3. **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**.