The radius of the cylinder is 5 cm, but its axial diagonal section is 20 cm. Find the height of the cylinder.
| February 5, 2021 | education
The axial section of the cylinder is a rectangle, since the cylinder is formed by the rotation of the rectangle around its side. For convenience we will designate it as AVSD.
The aircraft length is equal to two radii:
BC = r ∙ 2;
BC = 5 ∙ 2 = 10 cm.
The ABC triangle is rectangular, therefore, we apply the Pythagorean theorem:
AC ^ 2 = AB ^ 2 + BC ^ 2;
AB ^ 2 = AC ^ 2 – BC ^ 2;
AB ^ 2 = 20 ^ 2 – 10 ^ 2 = 400 – 100 = 300;
AB = √300 = 17.32 cm.
Answer: The height of the cylinder is 17.32 cm.
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