The radius of the base of the cylinder is 13, and its generatrix is 18. The section parallel to the axis of the cylinder

| May 22, 2021 | education

The radius of the base of the cylinder is 13, and its generatrix is 18. The section parallel to the axis of the cylinder is at a distance equal to 12. Find the area of the section.

Let’s take a look at the figure to solve.

We need to find the cross-sectional area ABED, which is (AD x AB).

AD = 18 cm by condition, as the generatrix of the cylinder.

To find AB, consider a right-angled triangle ACC1, in which AC is the radius of the base of the cylinder and is equal to 13 cm, CC1 is the distance from the axis of the cylinder to the section and is equal to 12 cm.

Then, by the Pythagorean theorem, AC1 ^ 2 = AC ^ 2 – CC1 ^ 2 = 13 ^ 2 – 12 ^ 2 = 169 – 124 = 25.

AC = 5 cm.

Then AB = 2 x AC = 10 cm.

Then SABED = (AD x AB) = 18 x 10 = 180 cm2.

Answer: The cross-sectional area is 180 cm2.



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