πr3=288π (∵ r = radius of sphere) ⇒r=6.....(1) OA is the radius of sphere
In ∆AOC,OA2=AC2+OC2⇒AC2=62−32
⇒AC=3√3cm (radius of circle formed) Curved surface area of bigger part = 3x Curved surface area of smaller part = x ⇒3x+x=4πr2⇒x=πr2 ⇒x=36π [From(1)] Total surface area of bigger part =3x+π(AC)2=108π+π(3√3)2 =(108+27)π=135πcm2