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 π. (1 point)

25 12 cubic meters

150 72 cubic meters

75 36 cubic meters

100.48 cubic meters

1 answer

To find the volume of a cone, we can use the formula:

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

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

First, we need to find the radius. Given that the diameter of the cone is 4 meters, the radius \( r \) is:

\[ r = \frac{4}{2} = 2 \text{ meters} \]

The height \( h \) is given as 6 meters.

Now, we can substitute the values into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 \]

Calculating \( (2)^2 \):

\[ (2)^2 = 4 \]

Now replacing this into the formula:

\[ V = \frac{1}{3} \times 3.14 \times 4 \times 6 \]

Calculating \( 4 \times 6 \):

\[ 4 \times 6 = 24 \]

Now substituting this back into the formula:

\[ V = \frac{1}{3} \times 3.14 \times 24 \]

Calculating \( 3.14 \times 24 \):

\[ 3.14 \times 24 = 75.36 \]

Finally, calculating \( \frac{75.36}{3} \):

\[ V = \frac{75.36}{3} = 25.12 \text{ cubic meters} \]

The volume of sand needed to fill the mold is 25.12 cubic meters.

Thus, the answer is:

25.12 cubic meters.