Final answer:
To fill a cone-shaped mold with a diameter of 4 meters and a height of 6 meters, use the formula V = πr²h, where π is 3.14. Calculating with a radius of 2 meters, the volume of sand required is 75.36 cubic meters.
Step-by-step explanation:
The volume of sand needed to fill a cone-shaped sandcastle mold can be calculated using the formula for the volume of a cone, which is V = πr²h, where V is the volume, r is the radius of the cone's base, and h is the height of the cone. To start, we need to find the radius of the cone by dividing the diameter by 2. Since the diameter is 4 meters, the radius (r) is 2 meters. Then, we use the given height (h) of 6 meters and π as 3.14 to calculate the volume.
Volume Calculation:
V = πr²h = 3.14 × (2 m)² × 6 m
V = 3.14 × 4 m² × 6 m = 3.14 × 24 m³
V = 75.36 m³
Therefore, the volume of sand required to fill the mold is 75.36 cubic meters (m³).