I have a question about three dimensional figures....Help?

Question

Are not all cubes similar?

Are all prisms similar?

Are all spheres similar?

Are not all cylinders similar?

Why or why not?

Answer 1

This depends on your definition of "similar".

The only ones I think are similar are  cubes and spheres.

Cubes only have one variable, the length of the side.

Spheres only have one variable, the radius.

Thus, they're all proportional to the one variable.

Prisms can vary in length, width, height, and shape.

(triangular, rectangular)

cylinders can vary in height and diameter.

Answer 2

all cubes are similar because all faces of a cube are squares.  Any one square is similar to another.

all spheres are similiar.

All prisms are not.  One prism may have a square base, and another may have a triangular base.  In that case they are not similar, so you can't say "all prisms are similar".

Similarly... all cylinders are not similar.  One could be very short and fat, and another could be very tall and thin.  In order for all the cylinders to be similar, there would have to be a similar ratio between the the height and the base for all cylinders.