A sandcastle mold is in the shape of a cone, with a diameter of 4 meters and a height of 6 meters. What volume of sand is needed to fill the mold? Use 3.14 for . (1 point) 75.36 cubic meters 25.12 cubic meters 150.72 cubic meters 100.48 cubic meters
To calculate the volume of a cone, we use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where
\( V \) is the volume,
\( \pi \) is Pi, which we will use as 3.14,
\( r \) is the radius of the base of the cone,
and \( h \) is the height of the cone.
Given that the diameter of the cone is 4 meters, the radius \( r \) is half of that, which is 2 meters.
The height \( h \) of the cone is given as 6 meters.
Now we can plug in the values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 \]
\[ V = \frac{1}{3} \times 3.14 \times 4 \times 6 \]
\[ V = \frac{1}{3} \times 12.56 \times 6 \]
\[ V = 4.18666667 \times 6 \]
\[ V = 25.12 \text{ cubic meters} \]
So, the volume of sand needed to fill the mold is 25.12 cubic meters.