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)# ?

Question

2080 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-21T20:10:15

This proposition is false...

Suppose the sphere has radius #r# and the cube side #t#.

Since the surface areas are equal, we have:

#4pi r^2 = 6t^2#

So #(r/t)^2 = 3/(2pi)# and #(r/t)^3 = (3/(2pi))^(3/2)#

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.