The objective of thermal insulating containers is to minimize heat exchange with the external environment. This heat exchange is proportional to the thermal conductivity k and the internal area of the container's faces, as well as to the difference in temperature between the external environment and the interior of the container, in addition to being inversely proportional to the thickness of the faces.
In order to evaluate the quality of two containers A ($40 \mathrm{~cm} \times 40 \mathrm{~cm} \times 40 \mathrm{~cm}$) and B ($60 \mathrm{~cm} \times 40 \mathrm{~cm} \times 40 \mathrm{~cm}$), with faces of the same thickness, a student compares their thermal conductivities $\mathrm{k}_{\mathrm{A}}$ and $\mathrm{k}_{\mathrm{B}}$. To do this, she suspends identical blocks of ice at $0^{\circ}\mathrm{C}$ inside each container, so that their surfaces are in contact only with air. After a time interval, she opens the containers while both still contain some ice and verifies that the mass of ice that melted in container $\mathbf{B}$ was twice that which melted in container $\mathbf{A}$.
The ratio $\frac{k_{A}}{k_{B}}$ is closest to
(A) 0.50.
(B) 0.67.
(C) 0.75.
(D) 1.33.
(E) 2.00.