SOLUTION: Two solid spheres have surface areas 144 pi sq.cm and 256 pi sq.cm, respectively. They are melted and recast to form a larger sphere. Find the surface area of this sphere in sq.cm.

Click here to see ALL problems on Surface-area

Question 388011: Two solid spheres have surface areas 144 pi sq.cm and 256 pi sq.cm, respectively. They are melted and recast to form a larger sphere. Find the surface area of this sphere in sq.cm.
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Two solid spheres have surface areas 144 pi sq.cm and 256 pi sq.cm, respectively. They are melted and recast to form a larger sphere. Find the surface area of this sphere in sq.cm.
---------------------
Find the radii, then the volumes.
Add the volumes, find the radius of the total.
Find the surface area of the total.
--------------

for 144pi sq cm, r = 6
for 256pi sq cm, r = 8
----------------

for r = 6, V = 288pi cc
for r = 8, V = 2048pi/3 cc
Total volume = 2912pi/3 cc
r =~ 8.996 cm
SA total =~ 1016.945 sq cm
----------------
=~ 323.7pi sq cm, less the the sum of the 2 original areas