Question

A cube and a sphere have equal total surface area. Find the ratio of the volume of sphere and cube.

Answer 1

Answer:

Let radius of sphere =r and Side of cube =a, then

4πr^2 =6a ^2  

⇒(  a /r) ^2 =   6/  4π

⇒(  a /r  )^2 =   6  /4π

⇒r /a =  1 /2root6 /π

Ratio of Volumes =  4/3πr^3/a^3

=  4/3π(r/a)^3

=4/3π*6/4π*1/2root6/π

=root6:rootπ

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