Question

please explain

a sphere and a cube have the same surface area Show that the ratio of the volume of sphere to that of cube is √6:√π.

Answer 1

Surface area of sphere = 4πr^2
Surface area of cube= 6a^2
According to question
4πr^2=6a^2
a^2=4πr^2/6
a=√4πr^2/√6
a=2r√π/√6 --------------(eq 1)

Now volume of sphere=4/3πr^3
Volume of cube=a^3
Ratio of volumes=volume of sphere/volume of cube
= 4/3πr^3/a^3
Putting the value of eq 1 we get
4/3πr^3/ 8r^3*π*√π /6√6
On solving further you will get. √6:√π

Hope it helps :)