Math CentralQuandaries & Queries


Question from Rohit, a student:

why isn't volume of a sphere = Area of a semicircle x the circumference.
i.e. if we revolve a semicircle around its axis we get a sphere

Hi Rohit,

Look at the semicircle below and imagine that it revolves around the horizontal axis to form a sphere.


The distance travelled by the red dot at the top is almost the length of the circumference of the circumference of the sphere but the distance travelled by the red dot close to the center is much less.

If each point in the semicircle travels a distance which is the circumference then you obtain half a circular cylinder

half cylinder

and its volume is area of the semicircle times the circumference.


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