SOLUTION: Two spheres of the same density have a ratio of 4 to 9 in surface area. If the small sphere weighs 10 lb. what does the sphere weigh? Thanks

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Question 626129: Two spheres of the same density have a ratio of 4 to 9 in surface area. If the small sphere weighs 10 lb. what does the sphere weigh?
Thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two spheres of the same density have a ratio of 4 to 9 in surface area.
If the small sphere weighs 10 lb. what does the sphere weigh?
:
Surface area of the two spheres;
r1= radius of the small sphere
r2= radius of the larger sphere
%284%2Api%2Ar1%5E2%29%2F%284%2Api%2Ar2%5E2%29 = 4%2F9
cancel 4*pi
%28r1%5E2%29%2F%28r2%5E2%29 = 4%2F9
:
%28r1%29%2F%28r2%29 = sqrt%284%2F9%29
therefore
r1 = 2
r2 = 3
:
Vol is equiv of weight here
let w = weight of the larger sphere
%28%284%2F3%29pi%2A2%5E3%29%2F%28%284%2F3%29pi%2A3%5E3%29 = 10%2Fw
Cancel %284%2F3%29pi and you have:
8%2F27 = 10%2Fw
cross multiply
8w = 27*10
w = 270%2F8
w = 33.75, the weight of the larger sphere