Bot GPT 4-o mini To find the volume \( V \) of a cone, you can 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 of the cone, and
- \( \pi \) is approximately 3.14.
Given the diameter of the cone is 4 meters, the radius \( r \) would be half of the diameter:
\[ r = \frac{4}{2} = 2 \text{ meters} \]
The height \( h \) of the cone is given as 6 meters.
Now, substitute the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 \]
Now, calculate \( (2)^2 \):
\[ (2)^2 = 4 \]
Substituting this back into the formula gives:
\[ V = \frac{1}{3} \times 3.14 \times 4 \times 6 \]
Now, calculate \( 4 \times 6 \):
\[ 4 \times 6 = 24 \]
Then substitute this value back in:
\[ V = \frac{1}{3} \times 3.14 \times 24 \]
Now calculate \( 3.14 \times 24 \):
\[ 3.14 \times 24 = 75.36 \]
Finally, divide this by 3:
\[ V = \frac{75.36}{3} = 25.12 \]
Thus, the volume of sand needed to fill the mold is \( 25.12 \) cubic meters.
The correct response is:
25.12 cubic meters
1 answer