Rotating the rectangle around its side creates a cylinder. The cylinder surface consists of a lateral surface and two cylinder bases.
In our example, the height of the cylinder is h = 5 cm, the radius of the bases is r = 7 cm.
Let us find the area of the lateral surface of the cylinder:
Side = 2 * Pi * r * h = 2 * Pi * 7 * 5 = 70 * Pi (cm2).
Find the surface areas of the two bases of the cylinder:
Sop = 2 * Pi * r ^ 2 = 2 * Pi * 7 ^ 2 = 98 * Pi (cm2).
Find the total surface area of the cylinder:
S = Sbok + Sbn = 70 * Pi + 98 * Pi = 168 * Pi (cm2).
Answer: the total surface area of the rotation figure is 168 * Pi cm2.
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