Through the generatrix of the cylinder, two mutually perpendicular sections are drawn

| September 5, 2021 | education

Through the generatrix of the cylinder, two mutually perpendicular sections are drawn, the areas of which are 16 and 30 cm ^ 2. Find the side of the cylinder.

Let the chord length AB = X cm, and the chord BC = Y cm, then the sectional area CC1B1B = Y * BB1 = 16 cm2, and the sectional area AA1B1B = X * BB1 = 30 cm2. Then Y = 16 / BB1, X = 30 / BB1.

Since the sections are perpendicular, the triangle ABC is rectangular, and then the hypotenuse of the AC coincides with the diameter of the circle at the base of the cylinder.

Then, by the Pythagorean theorem, AC ^ 2 = BC ^ 2 + AB ^ 2 = Y ^ 2 + X ^ 2 = (16 / BB1) ^ 2 + (30 / BB1) ^ 2 = (16 ^ 2 + 30 ^ 2) / BB1 ^ 2.

(2 * R) ^ 2 = (16 ^ 2 + 30 ^ 2) / BB1 ^ 2.

(2 * R) ^ 2 = 1156 / BB1 ^ 2.

2 * R = 34 / BB1.

R * BB1 = 34/2 = 17.

Let us determine the area of ​​the lateral surface of the cylinder.

Side = 2 * n * R * BB1 = 2 * n * 17 = n * 34 cm2.

Answer: The lateral surface area is equal to n * 34 cm2.



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