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.
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Find the radii, then the volumes.
Add the volumes, find the radius of the total.
Find the surface area of the total.
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{{{Area = 4*pi*r^2}}}
for 144pi sq cm, r = 6
for 256pi sq cm, r = 8
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{{{Vol = 4*pi*r^3/3}}}
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
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=~ 323.7pi sq cm, less the the sum of the 2 original areas