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Similarly the vase s cross section is a radius r circle with a radius h circle cut out so its area is pi r 2 pi h 2 as claimed.
Sphere cross section. The radius of the cross section can only be less than the radius of the sphere. The vertical cross section through the center of this torus is two circles. L x y z.
The size of the circle is maximized when the plane defining the cross section passes through a diameter. This may be proved by inscribing a cone upside down into semi sphere noting that the area of a cross section of the cone plus the area of a cross section of the sphere is the same as the area of the cross section of the circumscribing cylinder and applying cavalieri s principle. The radius of the cross section can be less than or equal to the radius of the sphere.
X 1 t y 1 4t z 3 5t this line passes through the circle center formed by the plane and sphere intersection in order to find the center point of the circle we substitute the line equation into the plane equation. The radius of the cross section can only be equal to the radius of the sphere. 1 t 4 1 4t 5 3 5t 6 0.
Indeed the slice usually called cross section of the sphere is a circle of radius sqrt r 2 h 2 which has area pi r 2 h 2. In physics the cross section is a measure of probability that a specific process will take place in a collision of two particles. Cross sections are usually parallel to the base like above but can be in any direction.
And the horizontal cross section is an annulus. Any cross section through a sphere is a circle or in the degenerate case where the slicing plane is tangent to the sphere a point. The radius of the cross section can be greater than less than or equal to the radius of the sphere.
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