To find the volume of the sandcastle mold, which is in the shape of a cone, 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 of the cone,
- \( h \) is the height of the cone.
- First, we need to find the radius. The diameter is given as 4 meters, so the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{4}{2} = 2 \text{ meters} \]
-
The height \( h \) of the cone is given as 6 meters.
-
Now, we can substitute the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 \]
- Calculate \( (2)^2 \):
\[ (2)^2 = 4 \]
- Substitute this back into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 4 \times 6 \]
- Calculate \( 4 \times 6 \):
\[ 4 \times 6 = 24 \]
- Now, substitute and calculate:
\[ V = \frac{1}{3} \times 3.14 \times 24 \]
- Calculate \( 3.14 \times 24 \):
\[ 3.14 \times 24 = 75.36 \]
- Finally, divide by 3:
\[ V = \frac{75.36}{3} = 25.12 \]
Thus, the volume of sand needed to fill the mold is:
\[ \boxed{25.12} \text{ cubic meters} \]