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The masses of two similar solids A and B are 20kg and 67.5kg respectively.
Given that the surface area of the solid A is 1080cm2 ,calculate the surface area of solid B
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As worded, printed, posted and presented, this problem is INCOMPLETE and, therefore, is INCORRECT.
To be correct, it must say, that in addition to geometric similarity, the solids are made of the same material.
So, my solution is for this MODIFIED formulation.
If material is the same, then, since its density is the same, the ratio of volumes
is the same as the ratio of masses, which is
= 3.375 times (the greater to the smaller).
Due to geometric similarity, it implies that the corresponding linear dimensions are in ratio
= 1.5 times (the greater to the smaller).
Hence, the ratio of surface areas is the square of the ratio of the corresponding linear dimensions
= = = 2.25.
From this proportion, the surface area of solid B is
= 1080*2.25 = 2430 cm^2. ANSWER
Solved, answered and explained.