Final answer:
The mass of A is proportional to its surface area when compared to solid B's surface area and mass. After solving the proportion, A's mass is approximately 4784.32 grams, with the closest answer choice being 4900 grams.
Step-by-step explanation:
The question involves comparing the masses of two similar solids based on their respective surface areas. Since the solids are made from the same material, their densities remain constant. This allows us to infer that their masses should be in the same ratio as their surface areas. The surface area of B is given as 40.32 cm² and its mass is 6912 grams, while the surface area of A is given as 28 cm².
To find the mass of A, we can set up a ratio comparing the surface areas to their respective masses:
A's surface area / B's surface area = A's mass / B's mass
28 / 40.32 = A's mass / 6912
After cross-multiplication and solving for A's mass, we get:
(28 / 40.32) × 6912 = A's mass
A's mass ≈ 4784.32 grams
The closest round number from the options given, when considering significant figures, is 4900 grams (Option A), which would be the completed mass of A.