Answered

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

Verified Answer :

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 = \(\frac{1}{3}\) 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 = \(\frac{1}{3}\) base area height = \(\frac{1}{3}*\pi r^2\) height

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

So volume of cone becomes =  \(\frac{1}{3}*\pi r^2\) 3 h= \(\pi r^2\) h

Hence Volume of cone Z = Volume of cylinder Y