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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

Verified Answer :

antonsandiego

Сone Z and Cylinder Y have the same volume. 
V=1/3πR²*H

vicobusso

Answer:

Cone Z and Cylinder Y

Step-by-step 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

\(V=\frac{1}{3}*h_{N}*B\)

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

\(V=\frac{\pi*r^{2}*h_{Z}}{3}\)

Where r is the radio and h is height.

  • Cylinder Y

\(V=\frac{\pi*r^{2}*h_{Q}}{3}\)

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

\(V=\frac{\pi*r^{2}*h_{Q}}{3}\)

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

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