To determine the volume of the cone shown in the diagram, we can use the volume formula for a cone:

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

where:

• $r$ is the radius of the base of the cone,
• $h$ is the height of the cone.

Given Values

From the diagram:

• The radius $r = 5 \, \text{cm}$.
• The slant height $s = 13 \, \text{cm}$.
• The horizontal distance from the center to the edge is $12 \, \text{cm}$, which represents the height $h$ of the cone.

Calculation

1. Substitute the values into the formula: $V = \frac{1}{3} \pi (5)^2 (12)$
2. Calculate $r^2$: $5^2 = 25$
3. Calculate $V$: $V = \frac{1}{3} \pi \cdot 25 \cdot 12$
4. Simplify: $V = \frac{1}{3} \pi \cdot 300$
5. Further calculation: $V = 100 \pi \approx 314.2 \, \text{cm}^3$

Answer

The closest answer to the volume is: (A) 314.2 cm³

Would you like a further breakdown of the steps or have any questions?

Here are some related questions to consider:

1. What is the formula for the surface area of a cone, given its slant height?
2. How would the volume change if the radius doubled but the height remained the same?
3. Can the Pythagorean theorem verify the height in this cone diagram?
4. What would be the effect on volume if both radius and height were halved?
5. How does the volume formula of a cone relate to that of a cylinder?

Tip: Remember, the volume of a cone is always one-third of a cylinder with the same base and height.