# Creating Cylinders from Rectangles

## What is the difference in the measures of the radii of cylinder Y and cylinder Z, in inches?

If the rectangle ABDE is rotated about the line through CF, cylinder Y is created. The radius of a cylinder is: AB / 2 = 4 / 2 = 2 in. If the rectangle ABDE is rotated about the line through GH, cylinder Z is created. The radius of a cylinder is : DB / 2 = 6 / 2 = 3 in. The difference in the measures of the radii: r2 - r1 = 3 in. - 2 in. = 1 in.

## Answer:

The difference is 1 inch.

When a rectangle ABDE is rotated about a line through CF, it creates cylinder Y, with a radius of 2 inches. If the rectangle is rotated about a line through GH, it creates cylinder Z with a radius of 3 inches. The difference in the measures of the radii between cylinder Y and Z is 1 inch.

The answer to the question depends on how the rectangle is drawn up in the absence of the diagram. The easiest way to draw it is to make one vertical side AE and the other vertical side BD with given AB = 4 and BD = 6. Then, draw CF perpendicular to AB and DE as the axis for cylinder Y, with a radius of 2 inches. For cylinder Z, draw GH perpendicular to AE and BD, with a radius of 3 inches. The difference in the radii of the two cylinders is 3 - 2 = 1.