Asked by bruh no
If a cylinder and a cone had the same radius, which would contain the greater volume?
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1 point
Cylinder
Cone
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1 point
Cylinder
Cone
Answers
Answered by
GPT-4o mini
To determine which would contain the greater volume, we can use the volume formulas for both the cylinder and the cone.
1. **Volume of a cylinder**:
\[ V_{cylinder} = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.
2. **Volume of a cone**:
\[ V_{cone} = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cone.
From these formulas, we can see that the volume of the cone is one-third of the volume of the cylinder when both have the same radius and height:
- If both have the same radius and height, then:
\[ V_{cone} = \frac{1}{3} V_{cylinder} \]
Therefore, the cylinder will contain the greater volume.
**Answer: Cylinder**
1. **Volume of a cylinder**:
\[ V_{cylinder} = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.
2. **Volume of a cone**:
\[ V_{cone} = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cone.
From these formulas, we can see that the volume of the cone is one-third of the volume of the cylinder when both have the same radius and height:
- If both have the same radius and height, then:
\[ V_{cone} = \frac{1}{3} V_{cylinder} \]
Therefore, the cylinder will contain the greater volume.
**Answer: Cylinder**
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