Question

what is the volume of this cone? diameter 22 mm height 19 mm round your answer to the nearest hundredth. use pie = 3.14

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, and \( h \) is the height.

1. **Find the radius**: The diameter of the cone is 22 mm, so the radius \( r \) is:

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

2. **Use the height**: The height \( h \) of the cone is given as 19 mm.

3. **Plug in the values into the volume formula**:

\[
V = \frac{1}{3} \times 3.14 \times (11)^2 \times 19
\]

4. **Calculate \( (11)^2 \)**:

\[
(11)^2 = 121
\]

5. **Now substitute that into the volume formula**:

\[
V = \frac{1}{3} \times 3.14 \times 121 \times 19
\]

6. **Calculating \( 121 \times 19 \)**:

\[
121 \times 19 = 2299
\]

7. **Now substitute back into the volume formula**:

\[
V = \frac{1}{3} \times 3.14 \times 2299
\]

8. **Calculate \( 3.14 \times 2299 \)**:

\[
3.14 \times 2299 = 7210.86
\]

9. **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.