According to Cavaliers principal, a right cylinder and a right rectangular prism can never have the same volume because they have different shapes. a. True
b. False

Explanation:

If you have the two 3D solids with cross sections of equal area, and they are of the same height, then it can be proven the two volumes are the same. So it is possible for a cylinder and triangular prism to have the same volume.

An example would be that imagine you had a stack of pennies to form a large cylinder. The volume is found by computing the area of one penny's face (aka area of a circle) multiplied by the height of the stack.

Now imagine moving the stack to form a strange curve of any sort you want. The pillar has a bend in it now. It's no longer a perfect cylinder, but we still have the same volume since we haven't destroyed any of the pennies.

All we've done is move things around. The small pieces all have the same volume, so the total volume is still the same as well. So this is one application of Cavalieri's principle.

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .