Math CentralQuandaries & Queries


Question from Sania, a student:

If the number of square centimeters on the surface area of a sphere is equal to the number of cubic centimeters in its volume find its diameter

Hi Sania,

We received a similar question some time ago but it was about the area and circumference of a circle. The question seems strange to me, why would anyone be interested in such a circle or sphere? Anyway that is the problem and how do you solve it?

The expressions for the surface area of a sphere and the volume of a sphere are usually given in terms of $r,$ the radius of the sphere. Set the expressions equal to each other and then solve for $r.$ The diameter is then twice the radius.

If you don't know the expressions ask Google. Type surface area of a sphere into the Google search window and see what results. Do the same for the volume.

I hope this helps,

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