a sphere is sliced by a plane that does not go through the center of the sphere. what is the shape of the…
a sphere is sliced by a plane that does not go through the center of the sphere. what is the shape of the cross section created by the slice? hemisphere semicircle circle oval
Answer
Explanation:
Step1: Recall Sphere Cross - Section
A sphere is a three - dimensional object. When a plane intersects a sphere, the set of points of intersection forms a two - dimensional figure.
Step2: Analyze the Plane Not Through Center
For a sphere, any plane that intersects it (whether it passes through the center or not) will form a circular cross - section. If the plane passes through the center, the circle has the maximum possible radius (equal to the radius of the sphere). If the plane does not pass through the center, the cross - section is still a circle, just with a smaller radius. A hemisphere is a three - dimensional figure (half of a sphere), a semicircle is a one - dimensional arc (half of a circle), and an oval is a different type of conic section - like shape that is not formed by a plane cutting a sphere.