Question
Volume of Cones Quick Check
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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 π
.(1 point)
Responses
100.48 cubic meters
100.48 cubic meters
75.36 cubic meters
75.36 cubic meters
150.72 cubic meters
150.72 cubic meters
25.12 cubic meters
Answers
GPT-4o mini
To find the volume of a cone, you can use the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cone.
Given:
- The diameter of the cone is 4 meters, so the radius \( r \) is \( \frac{4}{2} = 2 \) meters.
- The height \( h \) is 6 meters.
- Use \( \pi \approx 3.14 \).
Now plug in the values:
\[
V = \frac{1}{3} \times 3.14 \times (2^2) \times 6
\]
Calculating inside the parentheses:
\[
2^2 = 4
\]
So, we have:
\[
V = \frac{1}{3} \times 3.14 \times 4 \times 6
\]
\[
V = \frac{1}{3} \times 3.14 \times 24
\]
\[
V = \frac{3.14 \times 24}{3}
\]
\[
V = \frac{75.36}{3} = 25.12
\]
Thus, the volume of sand needed to fill the mold is **25.12 cubic meters**.
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cone.
Given:
- The diameter of the cone is 4 meters, so the radius \( r \) is \( \frac{4}{2} = 2 \) meters.
- The height \( h \) is 6 meters.
- Use \( \pi \approx 3.14 \).
Now plug in the values:
\[
V = \frac{1}{3} \times 3.14 \times (2^2) \times 6
\]
Calculating inside the parentheses:
\[
2^2 = 4
\]
So, we have:
\[
V = \frac{1}{3} \times 3.14 \times 4 \times 6
\]
\[
V = \frac{1}{3} \times 3.14 \times 24
\]
\[
V = \frac{3.14 \times 24}{3}
\]
\[
V = \frac{75.36}{3} = 25.12
\]
Thus, the volume of sand needed to fill the mold is **25.12 cubic meters**.