a = 16 cm;
b = 12 cm.
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
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