The height of the cylinder is 10. A section is drawn parallel to the axis of the cylinder, the chord of the section is equal to 6 cuts off the circumference of the base of the arc 90 degrees. Find the volume of the cylinder.
According to the condition, the chord A1B1 cuts off the arc, the degree measure of which is 900, then the central angle A1O1B1, which rests on this arc, is 90, and therefore the triangle A1O1B1 is rectangular and isosceles, since A1O1 and B1O1 are the radii of the circle.
Then, from the right-angled triangle A1O1B1, by the Pythagorean theorem, we determine the radius of the circle.
A1B1 ^ 2 = O1A1 ^ 2 + O1B1 ^ 2 = 2 * O1A1 ^ 2.
36 = 2 * O1A1 ^ 2.
O1A1 ^ 2 = 18.
О1А1 = R = 3 * √2 cm.
Determine the volume of the cylinder.
V = Sosn * OO1 = n * R ^ 2 * OO1 = n * (3 * √2) ^ 2 * 10 = 180 * n cm2.
Answer: The volume of the cylinder is 180 * n cm2.
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