If the surface area of a sphere and a cube are equal then how do you show that their volumes are in the ratio #sqrt(7) : sqrt(5)# ?
1 Answer
Mar 21, 2016
This proposition is false...
Explanation:
Suppose the sphere has radius
Since the surface areas are equal, we have:
#4pi r^2 = 6t^2#
So
Then:
#V_"sphere" / V_"cube"=(4/3 pi r^3)/t^3=4/3pi (r/t)^3 = 4/3pi (3/(2pi))^(3/2) ~~ 1.38197659788534191701#
Whereas:
#sqrt(7)/sqrt(5) ~~ 1.18321595661992320851#
So the proposition is false.