Question

A sphere and a cube have equal surface areas. What is the ratio of the volume of the sphere to that of the cube?

Answer 1

Surface area of sphere = sphere area of cube

i.e., 4πr² = 6a²

`r^2/a^2 = 6/(4pi)`

 `r/a = (6/(4x))^(1/2)`…… (i)

`"Now" , "volume of sphere"/"volume of cube" = (4/3pir^3)/a^3`

`v_1 /v_2 = (4pir^3)/(3a^3)`

      `=4/3 pi(r/a)(r/a)^2`

     `=4/3 pisqrt(6/pi) 1/2 6/pi`

`v_1/ v_2 = sqrt(6/pi)`

`v_1 :v_2 = sqrt(6/pi)`