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. 75.36 cubic meters
2. 100.48 cubic meters
3. 25.12 cubic meters
4. 150.72 cubic meters

1 answer

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

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

where \(r\) is the radius of the base of the cone, \(h\) is the height, and \(\pi\) is a constant approximately equal to 3.14 in this case.

  1. First, we need to find the radius. The diameter is given as 4 meters, so the radius \(r\) is:

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

  1. The height \(h\) of the cone is given as 6 meters.

  2. Now we can substitute these values into the volume formula:

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

  1. Calculate \( (2)^2 \):

\[ (2)^2 = 4 \]

  1. Then substitute that back into the equation:

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

  1. Compute \(4 \times 6\):

\[ 4 \times 6 = 24 \]

  1. Substitute this into the volume formula:

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

  1. Now calculate \(3.14 \times 24\):

\[ 3.14 \times 24 = 75.36 \]

  1. Finally, divide by 3:

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

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

\[ \text{Volume} = 25.12 \text{ cubic meters} \]

The correct answer is 3. 25.12 cubic meters.