To find the volume of the cone-shaped sandcastle mold, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height.
Given:
- The diameter of the cone is 4 meters, so the radius \( r \) is half of that: \[ r = \frac{4}{2} = 2 \text{ meters} \]
- The height \( h \) is 6 meters.
- Using \( \pi \approx 3.14 \).
Now, we can substitute the values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 \]
Calculating step by step:
-
Calculate \( r^2 \): \[ (2)^2 = 4 \]
-
Now substituting into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 4 \times 6 \]
-
Calculate \( 4 \times 6 \): \[ 4 \times 6 = 24 \]
-
Now substitute that into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 24 \]
-
Calculate \( 3.14 \times 24 \): \[ 3.14 \times 24 = 75.36 \]
-
Finally, calculate \( \frac{1}{3} \times 75.36 \): \[ V = \frac{75.36}{3} = 25.12 \]
Therefore, the volume of sand needed to fill the mold is: \[ \boxed{25.12} \text{ cubic meters} \]
So, the correct response is 25.12 cubic meters.