PH Algebra II - Lesson 8.6, Try This "c"

[Mrs Bee]

I think the book mixed up the formulas for the surface area of a sphere and for its volume. Try this "c" has: S=4π(r²), to be solved for r. This is the Surface formula. The solution in the back of the book makes no sense: r equals the square root of 3S over 4π. But things get more clear when one checks the Solution Key manual, which says r equals the third root of 3S over 4π, which would be the solution if the initial formula given had been the volume formula, V=4/3π(r³). So that's why I said there is confusion here with S and V.

[Cindy in Indy]

Hi Mrs. Bee,

I agree with your analysis.
For the given problem, with the formula for surface area given and asked to solve for r, the correct answer should be:
r = 1/2 [sqrt(S/pi)]
Note: I would simplify by pulling out the 4 from under the sqrt sign to get 1/2 out front.