Segment CD 25 cm, its ends lie on different circumferences of the cylinder base. find the distance from segment CD

| August 11, 2021 | education

Segment CD 25 cm, its ends lie on different circumferences of the cylinder base. find the distance from segment CD to the axis of the cylinder if its height is 7 cm and the diameter of the base is 26 cm

Let’s construct a projection of the inclined CD onto the lower base of the cylinder. Since AC is perpendicular to the base, the segment AD is the projection of the inclined CD, and the triangle ACD is rectangular.

Then, by the Pythagorean theorem, AD ^ 2 = CD ^ 2 – AC ^ 2 = 625 – 49 = 576.

AD = 24 cm.

Triangle ОАD is isosceles, since ОD = ОА as the radii of the base of the cylinder.

ОD = ОА = D / 2 = 26/2 = 13 cm.

Let’s build the height OH, which is also the median of the triangle AOD and is the shortest distance to the projection AD of the oblique CD, and therefore our desired value.

AH = AD / 2 = 24/2 = 12 cm.

Then, by the Pythagorean theorem, OH ^ 2 = AO ^ 2 – AH ^ 2 = 169 – 144 = 25.

OH = 5 cm.

Answer: From the axis of the cylinder to the straight line CD 5 cm.



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