Respuesta :
I have come to the conclusion that the answer would not be Cylinder Y nor Pyramid N bb.
Answer : Cone Z and Cylinder Y
Prism M and pyramid N have the same base area and the same height.
Volume of prism = base area * height
Volume of pyramid = [tex] \frac{1}{3}[/tex] * base area * height
cone Z has the same base area as cylinder Y, but it's height is three times the height of cylinder Y
So volume of prism and pyramid cannot be same.
Cylinder P and prism Q have the same height and the same base perimeter.
Volume of cylinder =base area * height= [tex] \pi r^2h [/tex]
Volume of prism = base area * height
The base area is not same as base perimeter so the volume of cylinder and prism cannot be same.
cone Z has the same base area as cylinder Y, but it's height is three times the height of cylinder Y
Volume of cylinder = base area * height = [tex] \pi r^2 * h [/tex]
Volume of cone = [tex] \frac{1}{3}[/tex] * base area * height = [tex] \frac{1}{3}*\pi r^2[/tex] * height
Given height of cone is three times the height of cylinder Y
So volume of cone becomes = [tex] \frac{1}{3}*\pi r^2[/tex] *3* h= [tex]\pi r^2[/tex] * h
Hence Volume of cone Z = Volume of cylinder Y
