The volume \(V_{\text{cylinder}}\) of a cylinder is given by the formula:
\[ V_{\text{cylinder}} = \pi r^2 h \]
where \(r\) is the radius and \(h\) is the height.
The volume \(V_{\text{cone}}\) of a cone with the same radius and height is given by:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
Since the volume of the cylinder is 33 cubic inches, we know:
\[ \pi r^2 h = 33 \, \text{cubic inches} \]
To find the volume of the cone, we use:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
Substitute the value from the cylinder's volume:
\[ V_{\text{cone}} = \frac{1}{3} \times 33 \, \text{cubic inches} = 11 \, \text{cubic inches} \]
So, the volume of the cone with the same radius and height is:
\[ 11 \, \text{cubic inches} \]
Therefore, the correct answer is:
\[ \boxed{11 \, \text{cubic inches}} \]
A cylinder has a volume of 33 cubic inches. What is the volume of a cone with the same radius and height?
A cylinder has a volume of 33 cubic inches. What is the volume of a cone with the same radius and height?
33 cubic inches
99 cubic inches
11 cubic inches
44 cubic inches
1 answer