If the volume V of a sphere with radius r is V=(4/3)πr^3. If the surface area is s=4πr^2, how can I express the volume as a function of the surface area S? My first thought was to set them equal to each other but it doesn't seem like the right thing to do. Any hints/help would be appreciated
-edit- ok so from S=4πr^2, I got r=√(S/4π)...So now I am stuck as to what to do. Since I'm trying to do V(S)=?...I just replaced the r from V=(4/3)πr^3 with √(S/4π) but the answer doesn't correlate with the answer on the book. what am i doing wrong?
Answer should be:S/6*sqrt(S/π)...what did i do wrong?
Special thanks to J.M for helping me figure this out