a sphere and a cube have equal surface areas the ratio..., Area & Volume, General Mathematics

Question:A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of the cube is :

A `√π : √6` 
B `√2 : √π` 
C `√ π: √3` 
D `√6 : √π`

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+ AnswerD

+ Explanation`4π R^2 = 6a^2 ⇒ R^2/a^2`

`= 3/(2π) ⇒ R/a`

`=(√3)/(√2π).`

`Volume of sphere/Volume of cube`

`= (4/3  πR^3)/a^3`

`= (4)/(3) π.(R/a)^3`

`= 4/3π . (3√3)/(2π√2π)`

`= (2√3)/(√2π)`

`= √12/√2π`

`= (√6)/(√π).`

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