In a cylinder with a height of 6 cm and a base radius of 5 cm, a section is drawn parallel to the OO1 axis

| March 31, 2021 | education

In a cylinder with a height of 6 cm and a base radius of 5 cm, a section is drawn parallel to the OO1 axis and at a distance of 4 cm from it to find the cross-sectional area.

Point O is the center of the lower base, O1 is the center.
Let’s measure 4 cm from the radius of the upper circle and draw a secant A1B1.
О1А1 = О1В1 = r = 5cm.
Let us omit from points A1 and B1 the perpendiculars, which are parallel, and therefore equal to the height of the cylinder:
AA1 = BB1 = h = 6cm.
It is necessary to find the sectional area АА1В1В:
S = AA1 * A1B1 = 6 * A1B1.
Let’s find A1B1.
To do this, consider a triangle A1O1B1, height O1C1 = 4 cm, A1C1 = A1B1 / 2.
By the Pythagorean theorem
A1C1 ^ 2 = O1A1 ^ 2 – O1C1 ^ 2 = 5 ^ 2 – 4 ^ 2 = 25 – 16 = 9cm ^ 2.
A1C1 = 3 cm.
This means that A1B1 = 2 * A1C1 = 2 * 3cm = 6cm.
So S = AA1 * A1B1 = 6cm * 6cm = 36cm ^ 2.



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