A sphere with a radius of 10 dm is crossed by a plane at a distance of 6 dm from the center.
| August 12, 2021 | education
A sphere with a radius of 10 dm is crossed by a plane at a distance of 6 dm from the center. find the cross-sectional area.
From point O, the center of the ball, draw a segment OA to the edge of the section. The OA segment is equal to the radius of the ball and, according to the condition, is equal to 10 dm.
The perpendicular ОВ to the diameter of the section forms a right-angled triangle AOB, from which, according to the Pythagorean theorem, we determine the radius AB of the section.
AB ^ 2 = OA ^ 2 – OB ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64.
AB = 8 cm.
Determine the cross-sectional area.
Ssection = n * AB ^ 2 = n * 8 ^ 2 = 64 * n cm2.
Answer: The cross-sectional area is 64 * n cm2.
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