This cylinder is cut by the plane shown. the plane is perpendicular to the base of the cylinder. what is the shape of the cross-section?

Rectangular

Step-by-step explanation:

Given that a cylinder is cut by a plane.

The plane is perpendicular to the base.

Imagine a graph with a line y=r

This will be a horizontal line.   When this is rotated between x=0 and x=h, we get a cylinder with radius =r and height =h.

When a plane cuts this cylinder the plane would be in xy plane a horizontal line.

So when a horizontal plane cuts the cylinder, we would get a planar closed shape which has opposite sides parallel and each angle 90 degrees.

Hence this will be a rectangle with length = h and width = r.

If h happens to be equal to r, in the special case, we may get a square.

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743