The volume of a cone is 27 cm^3. What is the volume of a cylinder that shares the same radius and height as the cone?(1 point)

cm^3

1 answer

The volume \( V \) of a cone is given by the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

where \( r \) is the radius and \( h \) is the height of the cone. Given that the volume of the cone is 27 cm\(^3\), we have:

\[ \frac{1}{3} \pi r^2 h = 27 \]

To find the volume of a cylinder that has the same radius and height as the cone, we use the volume formula for a cylinder, which is:

\[ V = \pi r^2 h \]

From the cone's volume formula, we know that:

\[ \pi r^2 h = 3 \times 27 = 81 \]

Thus, the volume of the cylinder is:

\[ \boxed{81} \text{ cm}^3 \]