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.
a 75.36 cubic meters
b 100.48 cubic meters
c 25.12 cubic meters
d 150.72 cubic meters
To calculate the volume of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
Where:
- \( V \) is the volume of the cone
- \( \pi \) is a constant (approximately 3.14)
- \( r \) is the radius of the cone's base
- \( h \) is the height of the cone
Given that the diameter of the cone is 4 meters, the radius \( r \) is half of the diameter, so:
\[ r = \frac{d}{2} = \frac{4 \text{ m}}{2} = 2 \text{ m} \]
The height \( h \) of the cone is 6 meters.
Substitute these values into the formula to find the volume:
\[ V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times 3.14 \times (2 \text{ m})^2 \times 6 \text{ m} \]
\[ V = \frac{1}{3} \times 3.14 \times 4 \text{ m}^2 \times 6 \text{ m} \]
\[ V = \frac{1}{3} \times 3.14 \times 24 \text{ m}^3 \]
\[ V = 3.14 \times 8 \text{ m}^3 \]
\[ V = 25.12 \text{ m}^3 \]
So the volume of sand needed to fill the mold is 25.12 cubic meters; therefore, the correct answer is:
c) 25.12 cubic meters