Question

a right cone is placed in an empty right cylinder. • the cone and the cylinder have the same height. • the circular bases of the cone and the cylinder have the same diameter. • the volume of the cone is 9 inches cubed. what is true about the volume of space in the cylinder surrounding the cone? complete the sentences by selecting the correct answers from the drop-down menus. the volume of space in the cylinder surrounding the cone is two times as great as the volume of the cone. the volume of the space in the cylinder surrounding the cone is choose... inches cubed. choose... 3 6 18 27

Explanation:

Step1: Recall volume formulas

The volume of a cylinder is $V_{cylinder} = \pi r^2 h$, and the volume of a cone is $V_{cone} = \frac{1}{3}\pi r^2 h$. Since the cone and cylinder have the same height ($h$) and same diameter (so same radius $r$), the volume of the cylinder is 3 times the volume of the cone.

Step2: Find the volume of the cylinder

Given $V_{cone} = 9$ in³, then $V_{cylinder} = 3\times9 = 27$ in³.

Step3: Find the surrounding volume

The volume of the space around the cone is $V_{cylinder}-V_{cone}=27 - 9=18$ in³. Also, the ratio of the surrounding volume to the cone's volume is $\frac{18}{9}=2$, so it's two times the cone's volume.

Answer:

The volume of space in the cylinder surrounding the cone is two times as great as the volume of the cone.
The volume of the space in the cylinder surrounding the cone is 18 inches cubed.