In a cylinder with a radius of 5 cm. drawn parallel to the axis of the section
| May 31, 2021 | education
In a cylinder with a radius of 5 cm. drawn parallel to the axis of the section, spaced from it at a distance of 3 cm. Find the height of the cylinder if the cross-sectional area is 64 cm2.
The AOB triangle is isosceles, the current is as OA = OB = R = 5 cm.
The distance OH, to the section ABCD, is the height and median of the isosceles triangle AOB, then AH = BH = AB / 2, and the triangle AOH is rectangular. Then, by the Pythagorean theorem, AH ^ 2 = OA ^ 2 – OH ^ 2 = 25 – 9 = 16.
AH = 4 cm, then AB = 2 * AH = 2 * 4 = 8 cm.
By condition, the cross-sectional area ABCD is 64 cm2. Since the section is a rectangle, then AB * AD = 64.
AD = 64 / AB = 64/8 = 8 cm.
Answer: The height of the cylinder is 8 cm.
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