Question

if a height is 12mm, diameter of 14, what is the volume in cubic millimeters of the cone.use 3.14 for pi. round your answer to the nearest hundredth

Answer 1

To find the volume \( V \) of a cone, you can use the formula:

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

where \( r \) is the radius, \( h \) is the height, and \( \pi \) is a constant.

1. **Calculate the radius**: The diameter is 14 mm, so the radius \( r \) is half of that:
\[
r = \frac{14}{2} = 7 \text{ mm}
\]

2. **Substitute the values into the volume formula**:
\[
V = \frac{1}{3} \times 3.14 \times (7)^2 \times 12
\]

3. **Calculate \( (7)^2 \)**:
\[
(7)^2 = 49
\]

4. **Now substitute \( 49 \) back into the volume formula**:
\[
V = \frac{1}{3} \times 3.14 \times 49 \times 12
\]

5. **Calculate \( 49 \times 12 \)**:
\[
49 \times 12 = 588
\]

6. **Substitute \( 588 \) into the volume formula**:
\[
V = \frac{1}{3} \times 3.14 \times 588
\]

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

8. **Now divide by 3**:
\[
V = \frac{1847.92}{3} \approx 615.9733333
\]

9. **Round to the nearest hundredth**:
\[
V \approx 615.97 \text{ cubic millimeters}
\]

Thus, the volume of the cone is approximately \( \boxed{615.97} \) cubic millimeters.