The ends of the chord of the lower base of the cylinder are removed from the center of the upper base by 15 cm

| January 11, 2021 | education

The ends of the chord of the lower base of the cylinder are removed from the center of the upper base by 15 cm, and the chord itself is removed from the center of the upper and lower bases by 13 cm and 5 cm, respectively. Find the area of the lateral surface of the cylinder.

The triangle OO1H is rectangular, then, according to the Pythagorean theorem, we define the leg OO1, which is the height of the cylinder. OO1 ^ 2 = O1H ^ 2 – OH ^ 2 = 169 – 25 = 144.
OO1 = 12 cm.
Let’s build the radius OA.
Triangle AOO1 is rectangular, in which, according to the Pythagorean theorem, we define the leg OA.
OA ^ 2 = O1A ^ 2 – OO1 ^ 2 = 225 – 144 = 81.
ОА = R = 8 cm.
Determine the length of the circle. L = 2 * π * R = 16 * π.
Then S side = L * OO1 = 16 * π * 12 = 192 cm2.
Answer: The lateral surface area is 192 cm2.



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