The radius of the base of the cylinder is 3 cm; the diagonal of the axial section is 7.5 cm. Find the height of the cylinder.
| February 9, 2021 | education
The axial section of the cylinder is a rectangle AВСD, whose side AD has the diameter of the circle at the base of the cylinder. AD = 2 * R = 2 * 3 = 6 cm.
The height of the cylinder is the leg AB of the AВD right-angled triangle.
By the Pythagorean theorem, AB ^ 2 = ВD ^ 2 – AD ^ 2 = 7.5 ^ 2 – 6 ^ 2 = 56.25 – 36 = 20.25.
AB = 4.5 cm.
Answer: The height of the cylinder is 4.5 cm.
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