The surface areas of two similar solids are 1,008cm^2 and 1,372cm^2. the volume of the larger solid is 1,801cm^3. find the volume of the smaller solid. round your answer to the nearest hundredth.

Question

Fiona

Mathematics

27 October, 10:15

The surface areas of two similar solids are 1,008cm^2 and 1,372cm^2. the volume of the larger solid is 1,801cm^3. find the volume of the smaller solid. round your answer to the nearest hundredth.

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Answers (1)

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Remington · Answer 1

Remember the ratios

Linear = a : b

Area = a^2 : b^2

Volume = a^3 : b^3

Hence area ratios are 1008 : 1372

Becomes linear ratios of Sqrt (1008) : sqrt (1372) : : 31.749 : 37.040

Volume ratios becomes 31.749^3 : 37.040^3 : : 32002.96 : 50817.46

Hence

32002.96 / 50817.46 = Vol (S) / 1801 cm^3

Vol (s) = 32002.96 X 1801 / 50817.46 = 1134.20cm^3 (nearest hundredth).