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)

Question

Responses

75.36 cubic meters
75.36 cubic meters

100.48 cubic meters
100.48 cubic meters

150.72 cubic meters
150.72 cubic meters

25.12 cubic meters

Answer 1

To calculate the volume of sand needed to fill a conical mold, you can use the formula for the volume of a cone:

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

where \( V \) is the volume, \( r \) is the radius of the base, \( h \) is the height, and \( \pi \) is Pi, approximately 3.14.

The diameter of the cone is given as 4 meters, so the radius (which is half the diameter) is:

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

The height of the cone is given as 6 meters.

Now plug the values into the volume formula:

\[ V = \frac{1}{3} \pi (2 \text{ meters})^2 (6 \text{ meters}) \]
\[ V = \frac{1}{3} \cdot 3.14 \cdot 4 \text{ meters}^2 \cdot 6 \text{ meters} \]
\[ V = \frac{1}{3} \cdot 3.14 \cdot 16 \text{ meters}^2 \cdot 6 \text{ meters} \]
\[ V = \frac{1}{3} \cdot 3.14 \cdot 96 \text{ meters}^3 \]
\[ V = 3.14 \cdot 32 \text{ meters}^3 \]
\[ V = 100.48 \text{ meters}^3 \]

The volume of sand needed to fill the mold is 100.48 cubic meters.