Answer:
Cone Z and Cylinder Y
Step-by-step explanation:
Complete Question:
Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base perimeter. cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y. Which two figures have the same volume?
Solution:
Volume of Cone is given by [tex]V_{cone}=\frac{1}{3}\pi r^2 h[/tex]
Volume of Cylinder is given by [tex]V_{cylinder}=\pi r^2 h[/tex]
It is given Cone Z has height that is 3 times that of Cylinder Y. Let Cylinder Y have height h ( from formula ), so Cone Z will have height "3h". So, Volume of Cone Z would be now:
[tex]V_{cone}=\frac{1}{3}\pi r^2 h\\V_{cone}=\frac{1}{3}\pi r^2 (3h)\\V_{cone}= \pi r^2 h[/tex]
Which is same as Volume of Cylinder Y!!
Thus, we can say Cone Z and Cylinder Y have same volume.
