# Determine the radius of the cylinder if the side sweep forms a rectangle 16 cm long and 12 cm wide.

Given:

Cylinder;

Rectangle;

a = 16 cm;

b = 12 cm.

r =?

Decision:

1) The sweep of the lateral surface of the cylinder is the lateral surface of the cylinder. Consequently, the sweep area is equal to the lateral surface area.

S div. = S side .;

Because the sweep is a rectangle. Therefore, the area of the scan is equal to the area of the rectangle. The area of a rectangle is equal to the product of its length and width.

S div. = S rectangle. = ab;

S side. = ab;

2) The lateral surface of a circular cylinder is equal to the product of the circumference of the base and the height.

S side. = 2πrh;

r = S side. / 2πh;

Let’s say the height of the cylinder is the width of the rectangle in the flat pattern of its lateral surface, i.e .:

h = b;

Substituting the letter values S side. and h into the formula for determining the radius of the cylinder, we get:

r = ab / 2πb;

r = a / 2π;

If a = 16, then r = a / 2π = 16 / 2π = 8 / π

Answer: 8 / π