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?(1 point)

1 answer

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

\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]

where \( r \) is the radius and \( h \) is the height of the cone.

Given that the volume of the cone is \( 27 , \text{cm}^3 \), we can express this as:

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

The volume \( V \) of a cylinder with the same radius and height is given by the formula:

\[ V_{\text{cylinder}} = \pi r^2 h \]

Notice that the volume of the cylinder can be related to the volume of the cone:

\[ V_{\text{cylinder}} = 3 \times V_{\text{cone}} \]

Substituting the volume of the cone:

\[ V_{\text{cylinder}} = 3 \times 27 = 81 , \text{cm}^3 \]

Therefore, the volume of the cylinder that shares the same radius and height as the cone is \( \boxed{81 , \text{cm}^3} \).