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Answer :
Final answer:
The mass of the larger sphere should be 1.953125 times that of the smaller sphere, calculated from the volumes based on their diameters. Given that the options provided in the question do not match the calculated answer, there seems to be an error in the question or answer choices.
Explanation:
The question involves finding the mass of the larger sphere using the mass of the smaller sphere and their respective diameters. Since both spheres are made of the same material, their masses are proportional to their volumes. The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. The radius is half of the diameter, so the radii of the two spheres are 2 m and 2.5 m, respectively.
Let's first calculate the volume of the smaller sphere (A) with diameter 4 m, which is V_A = (4/3)π(2)^3 = (4/3)π(8). The larger sphere (B) with diameter 5 m has a volume of V_B = (4/3)π(2.5)^3 = (4/3)π(15.625). Next, we find the ratio of their volumes, V_B / V_A = (15.625/8) = 1.953125.
Since the mass is proportional to the volume, the mass of the larger sphere will be 1.953125 times that of the smaller sphere. Therefore, if the smaller sphere has a mass of 120 kg, the mass of the larger sphere will be 120 kg * 1.953125 = 234.375 kg. However, this answer does not match any of the options provided in the question, suggesting that there may have been a mistake in the formulation of the problem or the given options. Therefore, I cannot provide a corresponding answer from the options a) through d).
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