SOLUTION: Hello, I need some help here. I think I know what the answer is, but I don't actually know the right path or format to get to it. Could you show me step by step? This is the prob

Algebra ->  Surface-area -> SOLUTION: Hello, I need some help here. I think I know what the answer is, but I don't actually know the right path or format to get to it. Could you show me step by step? This is the prob      Log On


   

Question 954120: Hello, I need some help here. I think I know what the answer is, but I don't actually know the right path or format to get to it. Could you show me step by step?
This is the problem: "Find the length of a radius of a sphere whose volume in cubic centimeters is equal to its surface area in square centimeters."
Thank you in advance.
Found 2 solutions by macston, hemu_da:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Volume=%284%2F3%29%28pi%29r%5E3
Surface area=4%28pi%29r%5E2
Set equations equal and solve for r:
%284%2F3%29%28pi%29r%5E3=4%28pi%29r%5E2 Divide each side by 4%28pi%29r%5E2
%281%2F3%29r=1 Multiply each side by 3
r=3 ANSWER: The radius of the sphere is 3 cm.
CHECK:
%284%2F3%29%28pi%29r%5E3=4%28pi%29r%5E2
%284%2F3%29%28pi%29%283%5E3%29=4%28pi%29%283%5E2%29
%284%2F3%29%28pi%29%2827%29=4%28pi%29%289%29
%284%2F3%29%2827%29pi=36%28pi%29
36%28pi%29=36%28pi%29

Answer by hemu_da(13) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of a sphere is (4/3)*pi*r*r*r.
And surface area is 4*pi*r*r.
Given
.
.
volume = surface area
Hence..
.
.
(4/3)*pi*r*r*r = 4*pi*r*r
.
After solving this...
.
.
r = 3...
Ans...