Ball diameter 2m. A plane is drawn through the end of the diameter at an angle of 45 degrees to it

| March 2, 2021 | education

Ball diameter 2m. A plane is drawn through the end of the diameter at an angle of 45 degrees to it. Find the length of the line intersecting the sphere with this plane.

Consider a right-angled triangle CBO, in which the legs СB and ВO are equal to the radius of the ball, and intersect at an angle of 90.

Then the hypotenuse of the BC, connecting the ends of the diameters of the ball and being the diameter of the section, is determined through the leg and the angle between the plane and the diameter.

OB / BC = CosOBC = Cos45.

ВС = OB / Cos45 = m / (√2 / 2) = m * √2 cm.

Then the length of the intersection line will be equal to the circumference of the BC diameter.

L = n * D = n * m * √2 cm.

Answer: The length of the intersection line is equal to n * m * √2 cm.



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