In the cylinder, a plane is drawn parallel to the cylinder axis, which cuts off the arc 2β from the circumference.

| September 5, 2021 | education

In the cylinder, a plane is drawn parallel to the cylinder axis, which cuts off the arc 2β from the circumference. The cutting plane intersects the base along a chord equal to a. The diagonal of the formed section makes an angle α with the generatrix of the cylinder. Find the cross-sectional area.

The section of a cylinder parallel to the axis of the cylinder is a rectangle, the length of one of which is equal, by condition, and cm.

In a right-angled triangle ABC, through the angle and length of one leg, we determine the length of the other leg. tgACB = AB / AC, AC = AB / tgα = a / tgα.

Determine the cross-sectional area.

Ssection = AC * AB = (a / tanα) * a = a ^ 2 / tanα = a ^ 2 * ctgα cm2.

Answer: The cross-sectional area is equal to a2 * ctgα cm2.



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