For equal volumes, the cube side L = (2π/3)1/3R ≈ 1.28R. Correspondingly, for a cube of this size,

Therefore, the cube is the safer shape for the farmer to use. This is basically because, in the same units, the surface area-to-volume ratio for the cube is 5/L ≈ 3.9/R, which exceeds the same ratio for the hemisphere, namely 3/R. (Again, it is assumed there is no heat lost through the base.)

AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.