A cone and a cylinder have the same base radius and the same height. If the volume of the cone is 10 cubic units, what is the volume of the cylinder? (1 point) 13 cubic units 33TT cubic units 30π cubic units 3.33m cubic units

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 of the base and \( h \) is the height.

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

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

Since the cone and the cylinder have the same base radius ( \( r \) ) and height ( \( h \) ), we can express the volume of the cylinder in relation to the volume of the cone.

From the volume of the cone, we know:

\[ 10 = \frac{1}{3} \pi r^2 h \]

To find the volume of the cylinder, we use the volume formula for the cylinder:

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

We can see that the volume of the cylinder is three times that of the cone:

\[ V_{cylinder} = 3 \times \text{Volume of cone} = 3 \times 10 = 30 \text{ cubic units} \]

Thus, the volume of the cylinder is:

\[ \boxed{30 \text{ cubic units}} \]