Through the chord of the base of the cylinder, the height of which is 12, and the radius of the base is 8

| April 28, 2021 | education

Through the chord of the base of the cylinder, the height of which is 12, and the radius of the base is 8, a section is drawn parallel to the axis of the cylinder. The angle between the radii drawn to the ends of this chord is 60 degrees. Find the cross-sectional area of the cylinder.

Since in the triangle AOB, according to the condition, OA = OB = R, then the triangle AРВ is isosceles.

If in an isosceles triangle one of the angles is 60, then such a triangle is equilateral, then in a triangle AOB. ОА = ОВ = AB = 8 cm.

Since the section АА1В1В is parallel to the axis of the cylinder, the side АА1 of the section is equal to the height of the cylinder. Then the cross-sectional area will be equal to: Ssection = AA1 * AB = 12 * 8 = 96 cm2.

Answer: The cross-sectional area is 96 cm2.



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