To solve for the approximate volume of the cone shown in the image, we use the formula for the volume of a cone:

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

Step 1: Identify the given values

• Radius of the base of the cone ($r$): $5 \, \text{cm}$ (from the image)
• Height of the cone ($h$): $6 \, \text{cm}$
• Approximation for $\pi$: $3.14$

Step 2: Plug in the values

$V = \frac{1}{3} \cdot 3.14 \cdot (5)^2 \cdot 6$

Step 3: Simplify the calculations

1. Compute $r^2$: $5^2 = 25$

2. Multiply by $h$: $25 \cdot 6 = 150$

3. Multiply by $\pi$: $150 \cdot 3.14 = 471$

4. Divide by 3: $\frac{471}{3} = 157$

Final Answer:

The approximate volume of the cone is: $\boxed{157 \, \text{cm}^3}$

Do you want further clarifications or detailed steps? Let me know!

Here are 5 related questions to explore further:

1. How is the formula for the volume of a cone derived?
2. What is the difference between the volume and surface area of a cone?
3. How would the volume change if the height doubled but the radius stayed the same?
4. How does the approximation of $\pi$ affect the accuracy of the volume calculation?
5. Can you find the volume of a cone if only the slant height and radius are given?

Tip: Always double-check your units when solving geometry problems to ensure accuracy!