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.

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

RELATED QUESTIONS
a solid metal sphere 12 cm in diameter is melted and recast into smaller solid metal... (answered by lwsshak3)

Two spheres M and N have a volume of 36 PI cubic cm and 972 PI respectively. What is the... (answered by Theo)

A solid metal ball of radius 2 cm is melted and the metal obtained recast to form a solid (answered by Fombitz,mananth)

two solid cylinder of radii 4 cm and 5 cm and length 6 cm and 4 cm respectively are... (answered by Fombitz)

A metal cylinder of base radius 4 cm and height 10 cm is melted and recast into spheres... (answered by josgarithmetic)

the volume and the curved surface area of a cylinder are 1650 cubic cm and 660 sq. cm... (answered by srinivas.g)

The volume and the total surface area of a spherical cone are 766 cu. cm. and 470 sq.... (answered by CPhill,ikleyn)

A solid cone of radius 5cm and height 8cm is melted and made into small spheres of radius (answered by Alan3354)