Question: Here's one that has me stumped:

I have a problem that stumped me.

The surface area and volume of a sphere are both equal to the product of 4-digit whole numbers and pi. What is the radius of the sphere?

Formulas:
SA Sphere = 4 pi r²
Vol Sphere = 4/3 pi r³

Any help would be greatly appreciated!

Starting with the surface area, let's say that
4pi(r²) = j(pi) where j is a whole number between 1000 and 9999.
Then r has to be a whole number as well.

1000 ≤ 4r² ≤ 9999
250 ≤ r²< 2500
15 < r < 50

Now let's look at the volume and define k(pi) = (4/3) pi (r³) where k
is a whole number between 1000 and 9999.

1000 ≤ (4/3)r³≤ 9999
750 ≤ r³< 7500
9 < r ≤ 19

Put these together and you end up with 16 ≤ r ≤ 19, but notice that
if (4/3)(r³) = a whole number, then r must be divisible by three.
That means 18 is the only possibility.
(4/3)(18³) = 7776.
4(18²) = 1296.

Stephen La Rocque.>