Question

NEED HELP PLEASE! WILL GIVE MEDAL:

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 it's height is three times the height of cylinder Y. Which two figures have the same volume?
Choices:
1) Prism M
Cylinder p
Cone Z
And
2)Pyramid N
Prism Q
Cylinder Y

Answer 1

I have come to the conclusion that the answer would not be Cylinder Y nor Pyramid N bb.

Answer 2

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 =
`(1)/(3)` * 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=
`\pi r^2h`

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 =
`\pi r^2 * h`

Volume of cone =
`(1)/(3)` * base area * height =
`(1)/(3)*\pi r^2` * height

Given height of cone is three times the height of cylinder Y

So volume of cone becomes =
`(1)/(3)*\pi r^2` *3* h=
`\pi r^2` * h

Hence Volume of cone Z = Volume of cylinder Y