It can be concluded from the below solution that the volume of cone Z, volume of cylinder P and the volume of prism M are same, that is:
[tex]\rm V=V''=V'''[/tex]
Given:
- 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.
Let the volume of prism M having base area be A and height be H is given by V that is:
[tex]\rm V = AH[/tex]
It is given that base area and height of pyramid N is same as the prism M therefore volume of pyramid will be:
[tex]\rm V' = \dfrac{1}{3}\times A \times H[/tex]
It is also given that base perimeter and height of cylinder P is same as the prism therefore volume of cylinder will be:
[tex]\rm V'' = A \times H[/tex]
It is also given that base area of cone Z is same as the cylinder P and its height is three times the height of cylinder Y. Therfore the volume of cone will be:
[tex]\rm V''' = \dfrac{1}{3}\times A\times(3H)[/tex]
[tex]\rm V''' = AH[/tex]
It can be concluded that volume of cone Z, volume of cylinder P and the volume of prism M are same, that is:
[tex]\rm V=V''=V'''[/tex]
For more information, refer the link given below:
https://brainly.com/question/1578538
