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Ball volume

Lecture





Using the formula for the volume of rotation bodies, we calculate the volume of the ball.

  Ball volume

We introduce Cartesian coordinates, taking the center of the ball to the origin. The xy plane intersects the surface of a sphere of radius R in a circle defined by the formula

  Ball volume

The semicircle located above the x axis is given by the equation

  Ball volume

Therefore, the volume of the ball is determined by the formula

  Ball volume

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Stereometry

Terms: Stereometry