Question

A model of a volcano has a height of 12 in., and a diameter of 12 in.
What is the approximate volume of the model?
Use 3.
14 to approximate pi, and express your final answer as a decimal.
Enter your answer as a decimal in the box.

Answer 1

To find the volume of a volcano model, we can assume it's in the shape of a cone. The volume \( V \) of a cone is calculated using the formula:

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

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

1. **Find the radius:**
Given the diameter is 12 inches, the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{12}{2} = 6 \text{ inches}
\]

2. **Use the height:**
The height \( h \) of the volcano model is given as 12 inches.

3. **Substitute the values into the volume formula:**
Using \( \pi \approx 3.14 \):

\[
V = \frac{1}{3} \times 3.14 \times (6^2) \times 12
\]

First, calculate \( r^2 \):

\[
r^2 = 6^2 = 36
\]

Now substitute \( r^2 \) and \( h \) into the equation:

\[
V = \frac{1}{3} \times 3.14 \times 36 \times 12
\]

4. **Calculate \( 36 \times 12 \):**

\[
36 \times 12 = 432
\]

5. **Now calculate \( \frac{1}{3} \times 3.14 \times 432 \):**

\[
V = \frac{1}{3} \times 3.14 \times 432 = \frac{3.14 \times 432}{3}
\]

First, calculate \( 3.14 \times 432 \):

\[
3.14 \times 432 = 1358.08
\]

Now divide by 3:

\[
V = \frac{1358.08}{3} \approx 452.6933
\]

6. **Round the final answer if necessary:**
Depending on the required precision, we can round to a reasonable decimal place. Let's round it to two decimal places.

\[
V \approx 452.69
\]

Therefore, the approximate volume of the model is:

\[
\boxed{452.69}
\]