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

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

where:

• $r$ is the radius,
• $h$ is the height,
• $\pi$ is approximately 3.14, if you're using a rounded value.

Given:

• $r = 3$ units,
• $h = 4$ units.

Step-by-Step Calculation:

1. Square the radius: $r^2 = 3^2 = 9$

2. Multiply the squared radius by the height: $9 \times 4 = 36$

3. Multiply the result by $\frac{1}{3} \pi$: $V = \frac{1}{3} \times 3.14 \times 36$

4. Simplify: $V = \frac{1}{3} \times 113.04 = 37.68$

So, the volume of the cone is approximately $37.68$ cubic units.

Final Answer:

$V \approx 37.68 \, \text{cubic units}$

Would you like further details or explanations?

Here are some related questions you can explore:

1. How does the formula for the volume of a cone change with different values of radius and height?
2. How do you derive the formula for the volume of a cone?
3. What is the difference between the volume of a cone and a cylinder?
4. How would the volume change if the radius was doubled?
5. How do you calculate the surface area of a cone?

Tip: Remember that the volume of any cone is proportional to the area of its base times the height, and the formula accounts for the tapering shape by including the factor $\frac{1}{3}$.