Question

PLEASE HELP I'LL 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

Cone Z and Cylinder Y

Explanation:

To know what's happening here you need to compare volume equations:

• Prism M

`V=B*h_(M)`

Where B is base area and h is height.

• Pyramid N

`V=(1)/(3)*h_(N)*B`

Where B is base area and h is height.

• Cylinder P

`V=\pi*r^(2)*h_(P)`

Where r is the radio and h is height.

• Prism Q

`V=B*h_(Q)`

Where B is base area and h is height.

• Cone Z

`V=(\pi*r^(2)*h_(Z))/(3)`

Where r is the radio and h is height.

• Cylinder Y

`V=(\pi*r^(2)*h_(Q))/(3)`

Where r is the radio and h is height, but you know
`h_(Y)` is the same as
`3*h_(Y)` so

`V=(\pi*r^(2)*h_(Q))/(3)`

And that's why Cone Z and Cylinder Y is the right answer.

Answer 2

Сone Z and Cylinder Y have the same volume.
V=1/3*π*R²*H