The volume of a cone is 27 cm3 . What is the volume of a cylinder that shares the same radius and height as the cone?
To find the volume of a cylinder with the same radius and height as the cone, we first need to determine the formula for the volume of a cone and a cylinder.
The volume of a cone is given by the formula:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
Given that the volume of the cone is 27 cm^3, we have:
\[ 27 = \frac{1}{3} \pi r^2 h \]
Next, the volume of a cylinder is given by the formula:
\[ V_{\text{cylinder}} = \pi r^2 h \]
Since the height and radius of the cylinder are the same as that of the cone, we can substitute in the values of height and radius from the cone into the formula for the volume of the cylinder:
\[ V_{\text{cylinder}} = \pi r^2 h \]
\[ V_{\text{cylinder}} = \pi r^2 \left(\frac{27}{\pi r^2}\right) \]
\[ V_{\text{cylinder}} = 27 \]
Therefore, the volume of the cylinder that shares the same radius and height as the cone is 27 cm^3.