AFCAT I 23 Jan 2025 Shift 1 Paper

Let the outer and the inner radii of the sphere be ' R ' cm and ' r ' cm respectively.
∵ Curved surface area of sphere =4π×(‌ radius ‌)2
‌⇒4πR2=324π
‌⇒R2=81
‌⇒R=√‌81=9cm
Now,
Volume of metal used = Volume of outer sphere - Volume of inner sphere
∵ Volume of sphere =4∕3×π×(‌ radius ‌)3
‌⇒684π=4∕3×πR3−4∕3×πr3
‌⇒3∕4×684=(9)3−r3
‌⇒r3=729−513=216
‌⇒r=6cm
∴ Thickness of hollow sphere =R−r=9−6=3cm