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 of a cone is given by the formula:

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

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

You mentioned that the volume of the cone is \( 27 , \text{cm}^3 \). Therefore,

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

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

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

To find the volume of the cylinder, we can relate it to the volume of the cone:

  1. Since the volume of the cylinder is three times the volume of the cone, because the volume of a cylinder is three times that of a cone with the same base and height:

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

  1. Substituting the volume of the cone:

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

Therefore, the volume of the cylinder is \( \boxed{81} , \text{cm}^3 \).