To find the volume of sand needed to fill the mold, which is in the shape of 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
- \( \pi \) is approximately 3.14
- \( r \) is the radius of the base
- \( h \) is the height of the cone
From the problem, we know:
- The diameter of the base is 4 meters, so the radius \( r \) is half of the diameter, which is \( \frac{4}{2} = 2 \) meters.
- The height \( h \) is 6 meters.
Now, plug these values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 \]
Calculate \( (2)^2 \):
\[ (2)^2 = 4 \]
Now, plug this value back in:
\[ V = \frac{1}{3} \times 3.14 \times 4 \times 6 \]
Multiply the numbers together inside the parentheses:
\[ 4 \times 6 = 24 \]
So, the equation now is:
\[ V = \frac{1}{3} \times 3.14 \times 24 \]
Next, multiply \( 3.14 \) by 24:
\[ 3.14 \times 24 = 75.36 \]
Finally, multiply by \( \frac{1}{3} \):
\[ V = \frac{1}{3} \times 75.36 = 25.12 \]
So, the volume of sand needed to fill the mold is \( 25.12 \) cubic meters.
Therefore, the correct answer is:
\[ 25.12 \text{ cubic meters} \]
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 ππ .(1 point) responses 25.12 cubic meters 25.12 cubic meters 75.36 cubic meters 75.36 cubic meters 150.72 cubic meters 150.72 cubic meters 100.48 cubic meters
1 answer