A sphere & a cube have equal surface area. Show that the ratio of volume of surface areas of sphere to that of cube is root6:root pi.

Asked by  | 10th Mar, 2013, 10:59: PM

Expert Answer:

Answer: Given : A sphere & a cube have equal surface area.
To Show : that the ratio of volume of surface areas of sphere to that of cube is 61/2: pi1/2
 
As the surface area of sphere is equal to that of cube
=> 4pi r2 = 6a2
=> r 2/a2 = 6/(4 pi)
=> r/a = 61/2/(2 pi1/2 )
 
The ratio of the vloume of sphere to cube is = [(4/3) pi r3 ] / (a3 )
                                                        
Putting the value of eq 1 , we get
vol of sphere/ vol of cube = [(4/3) pi ( 61/2 a/(2 pi1/2 ))3 ] / [a3 ]
                                      = (4 pi 63/2 ) / (3 * 8 pi3/2 )
                                      = 61/2 / pi1/2 
                              Hence proved

Answered by  | 11th Mar, 2013, 12:51: AM

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