Question

What is the volume, in cubic millimeters, of the cone? Use 3.14 for pi. Round your answer to the nearest hundredth.
height=12
diameter=14

Answer 1

wrong

Answer 2

To find the volume of a cone, we use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( r \) is the radius of the base, and \( h \) is the height.

Given:
- The height \( h = 12 \) mm
- The diameter \( d = 14 \) mm

First, we calculate the radius \( r \):

\[
r = \frac{d}{2} = \frac{14}{2} = 7 \text{ mm}
\]

Next, we can substitute the values of \( r \) and \( h \) into the volume formula. Using \( \pi \approx 3.14 \):

\[
V = \frac{1}{3} \times 3.14 \times (7^2) \times 12
\]

Calculating \( 7^2 \):

\[
7^2 = 49
\]

Now, substitute \( 49 \) into the formula:

\[
V = \frac{1}{3} \times 3.14 \times 49 \times 12
\]

Calculating \( 49 \times 12 \):

\[
49 \times 12 = 588
\]

Now substitute \( 588 \) into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 588
\]

Calculating \( 3.14 \times 588 \):

\[
3.14 \times 588 = 1847.92
\]

Now calculate \( \frac{1}{3} \times 1847.92 \):

\[
V = \frac{1847.92}{3} \approx 615.97
\]

Thus, the volume of the cone, rounded to the nearest hundredth, is:

\[
\boxed{615.97} \text{ cubic millimeters}
\]

Answer 3

Let’s re-calculate the volume of the cone step by step to ensure accuracy.

1. **Given Values**:
- Height \( h = 12 \) mm
- Diameter \( d = 14 \) mm

2. **Calculate Radius**:
\[
r = \frac{d}{2} = \frac{14}{2} = 7 \text{ mm}
\]

3. **Volume Formula**:
\[
V = \frac{1}{3} \pi r^2 h
\]

4. **Substituting Values**:
Use \( \pi \approx 3.14 \):
\[
V = \frac{1}{3} \times 3.14 \times (7^2) \times 12
\]

5. **Calculating \( r^2 \)**:
\[
r^2 = 7^2 = 49
\]

6. **Substitute \( r^2 \) into the Volume Formula**:
\[
V = \frac{1}{3} \times 3.14 \times 49 \times 12
\]

7. **Calculating \( 49 \times 12 \)**:
\[
49 \times 12 = 588
\]

8. **Final Calculation for Volume**:
\[
V = \frac{1}{3} \times 3.14 \times 588
\]

Calculate \( 3.14 \times 588 \):
\[
3.14 \times 588 = 1847.92
\]

Now divide by 3:
\[
V = \frac{1847.92}{3} = 615.97
\]

After recalculating each step, the final volume of the cone is again:

\[
\boxed{615.97} \text{ cubic millimeters}
\]

If there is a specific part you think is incorrect or if you have mentioned different parameters, please let me know, and I’ll assist you further!