In a cylinder with a height of 6 cm and a base radius of 5 cm, a section is drawn
| September 24, 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, find the cross-sectional area.
From point O we draw the radii ОА and ОВ of the base of the cylinder.
The AOB triangle is isosceles, then its height OH is also its median, and therefore AH = BH = AB / 2.
From the right-angled triangle AOH, by the Pythagorean theorem, we determine the length of the leg AH.
AH ^ 2 = AO ^ 2 – OH ^ 2 = 25 – 16 = 9.
AH = 3 cm.
Then AB = 2 * AH = 2 * 3 = 6 cm.
Section A1ABB1 is a rectangle, then its section is equal to: Ssection = AB * A1A = 6 * 6 = 36 cm2.
Answer: The cross-sectional area is 36 cm2.
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