Question

A cube and a sphere are made such that the total surface area of the cube is equal to the surface area of the sphere. Find the ratio between the radius of the sphere to the side of the cube if the ratio of the buoyant forces is X : Y.

Answer 1

consider a cube of side a

so total surface area of cube = 6$l^2$ .....................(1)

now let sphere has radius r

so total surface area of sphere = 4$\pi r^2$ ..................(2)

now according to question , 1st and 2nd are equal

so we have 6$l^2$ = 4$\pi r^2$

hence $\frac{r^2}{l^2}$ = $\frac{3}{2\pi }$

so $\frac{r}{l}$ = $(\frac{3}{2\pi }{)}^{0.5}$