Through the generatrix of the cylinder, two mutually perpendicular sections are drawn with the same area

| September 16, 2021 | education

Through the generatrix of the cylinder, two mutually perpendicular sections are drawn with the same area – 40 square units of measure. Determine the axial cross-sectional area of the cylinder.

Since the formed sections are mutually perpendicular, then at the base of the cylinder, the formed right angle AKD will rest on the diameter of the circle at the base of the cylinder.

Then the triangle AKD is rectangular and isosceles, AK = DK.

Then, on the Pythagorean theorem, AD ^ 2 = R ^ 2 = AK ^ 2 + DK ^ 2 = 2 * AK ^ 2.

AD = AK * √2 see (1).

The cross-sectional area of the AKMB is equal to: Skmv = AK * AB = 40 cm2.

The axial cross-sectional area ABCD is equal to:

Savsd = AD * AB. Instead of AD, substitute equation 1.

Savsd = AK * √2 * AB = Skmv * √2 = 40 * √2 cm2.

Answer: The axial section area is 40 * √2 cm2.



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