Find the surface area of the solid sphere formed

Question

Metallic spheres of radii 6cm, 8 cm and 10 cm respectively are melted and recasted into a single solid sphere. Taking pie=3.1, find the surface area of the sphere formed.

Answer 1

Volume of sphere=(4/3)πr^3 where r=radius.

The sum of the three volumes is (4/3)(6^3+8^3+10^3)π=2304π=(4/3)1728π=(4/3)(12^3)π.

If R is the radius of the reconstituted sphere then (4/3)πR^3=(4/3)(12^3)π, R=12cm.

Surface area=4πR^2=576π=1785.6 sq cm if π=3.1 approx.