The sweep of the lateral surface of the cylinder is a square with a diagonal of 10 cm.
| August 12, 2021 | education
The sweep of the lateral surface of the cylinder is a square with a diagonal of 10 cm. Find the area of the lateral surface of the cylinder
A cylinder is a geometric body created by rotating a rectangle around its side.
Since the sweep of the lateral surface of the cylinder is a square, its area is equal to the length of one of its sides in a square:
S = a ^ 2.
The length of the side of this sweep is calculated according to the principle of the Pythagorean theorem.
AC ^ 2 = AB ^ 2 + BC ^ 2.
Since AB = BC, then:
AB ^ 2 = BC ^ 2 = AC ^ 2/2;
AB ^ 2 = BC ^ 2 = 10 ^ 2/2 = 100/2 = 50 cm2.
The lateral surface area of this cylinder is 50 cm2.
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