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) Responses 75.36 cubic meters 75.36 cubic meters 150.72 cubic meters 150.72 cubic meters 100.48 cubic meters 100.48 cubic meters 25.12 cubic meters

1 answer

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

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

Where:

  • \( V \) is the volume,
  • \( r \) is the radius of the base,
  • \( h \) is the height of the cone.

From the problem:

  • The diameter of the cone is 4 meters, so the radius \( r \) is \( \frac{4}{2} = 2 \) meters.
  • The height \( h \) is 6 meters.

Now substituting the values into the formula:

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

Calculating the radius squared:

\[ 2^2 = 4 \]

So the formula now looks like:

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

Now calculate \( 4 \times 6 \):

\[ 4 \times 6 = 24 \]

Now, substituting back in:

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

Calculating \( 3.14 \times 24 \):

\[ 3.14 \times 24 = 75.36 \]

Now, finding \( \frac{1}{3} \times 75.36 \):

\[ V = \frac{75.36}{3} = 25.12 \]

Therefore, the volume of sand needed to fill the mold is:

\[ \boxed{25.12} \text{ cubic meters} \]