Given : The surface area of a cube = surface area of a sphere Length of cube =x The radius of the sphere =y Formula used : 1. Surface area of cube =6×( side )2 2. Surface area of sphere =4πr2 3. Volume of cube =side3 4. Volume of sphere =(4∕3)πr3 Formula used : 1. Surface area of cube =6×( side )2 2. Surface area of sphere =4πr2 3. Volume of cube =side3 4. Volume of sphere =(4∕3)πr3 Calculations : The surface area of a cube = surface area of a sphere Using equations (1) and (2), we get ⇒6x2=4πy2 ⇒x2∕y2=4π∕6 ⇒x2∕y2=(4∕6)×(22∕7) ⇒x2∕y2=44∕21 ⇒
x
y
=
√44
√21
If 2x>3y then, 4x2>9y2 ⇒4(√44)2>9(√21)2 ⇒4×44>9×21 ⇒176<189≠2x>3y Statement I is incorrect Using equations (3) and (4), we get ⇒ The volume of cube =(√44)3 ⇒44√44 unit 3=88√11 unit 3 ⇒ The volume of sphere =(4∕3)×(22∕7)×(√21)3 ⇒88√21unit3 The volume of a sphere is greater than the volume of a cube ∴ Neither statement 1 nor statement 2 is correct.