Question

what is the volume of this cone? diameter 22 mm height 19 mm round your answer to the nearest hundredth.

Answer 1

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**.