Question

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 pi.

100.48
75.36
25.12
150.72

Answer 1

To find the volume of the sandcastle mold shaped like a cone, 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 of the cone.

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

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

Now, substitute the radius and height into the volume formula. The height \( h \) is given as 6 meters.

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

Calculating \( (2)^2 \):

\[
(2)^2 = 4
\]

Now substituting this back into the volume formula:

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

Calculating \( 4 \times 6 \):

\[
4 \times 6 = 24
\]

Now substitute that back into the formula:

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

Calculating \( 3.14 \times 24 \):

\[
3.14 \times 24 = 75.36
\]

Now divide by 3:

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

The volume of sand needed to fill the mold is:

\[
\boxed{25.12}
\]