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