did I translate this question correctly.

Question

Translate this sentence into a mathematical equation:
The surface area S of a sphere is directly proportional to the square of its radius r.

 

I got s=4πr² 

 

did i translate this correctly?

Answer 1

you're absolutely right, but it appears that you may have used calculus.

 

without calculus, the sentence translation would only be S = kr² where k is some constant of proportionality.

 

finding out that k = 4times 'pi' is based on taking the derivative of the Volume formula, yielding dV = (4πr²)(dr)  and then visualizing this thin onionskin volume as a flattened-out volume with a Base Area 4πr²  times thickness 'dr' (or height).  Thus the Surface Area is 4πr²