At the base of the straight prism lies a right-angled triangle with legs 5 and 12. The lateral edges of the prism are equal to 3 / п. Find the lateral surface area of the described cylinder.
Since there is a right-angled triangle at the base of the prism, its hypotenuse is the diameter of the cylinder described near the prism.
By the Pythagorean theorem, in a right-angled triangle ABC, we determine the length of the hypotenuse AB.
AB ^ 2 = AC ^ 2 – BC ^ 2 = 144 + 25 = 169.
AB = 13 cm.
Then the radius of the base of the cylinder is: R = AB / 2 = 13/2 = 6.5 cm.
Determine the circumference at the base of the cylinder. L = 2 * π * R = 2 * π * 6.5 = 13 * π cm.
Then the area of the lateral surface of the cylinder is: Sside = L * AA1 = 13 * π * 3 / π = 39 cm2.
Answer: The area of the lateral surface of the cylinder is 39 cm2.
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