Question

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) cm³ check answer remaining attempts : 3

Explanation:

Step1: Recall volume formulas

The volume of a cone is \( V_{cone}=\frac{1}{3}\pi r^{2}h \), and the volume of a cylinder is \( V_{cylinder}=\pi r^{2}h \).

Step2: Relate the two volumes

We can see that \( V_{cylinder} = 3\times V_{cone} \) when they have the same radius \( r \) and height \( h \).

Step3: Calculate cylinder volume

Given \( V_{cone}=27\space cm^{3} \), then \( V_{cylinder}=3\times27 = 81\space cm^{3} \).

Answer:

\( 81 \)