Two solids are mathematically similar and have volumes cm81 3 and cm24 3 �The surface area of the smaller solid is cm44 2 �Calculate the surface area of the larger solid�
Question
Two solids are mathematically similar and have volumes cm81 3 and cm24 3 �The surface area of the smaller solid is cm44 2 �Calculate the surface area of the larger solid�
Solution
The ratio of the volumes of two similar solids is the cube of the ratio of their corresponding lengths. So, the ratio of the volumes is (81/24) = 27/8. The cube root of this ratio gives the ratio of the lengths, which is 3/2.
The ratio of the surface areas of two similar solids is the square of the ratio of their corresponding lengths. So, the ratio of the surface areas is (3/2)^2 = 9/4.
Therefore, if the surface area of the smaller solid is 44 cm^2, the surface area of the larger solid is 44 * (9/4) = 99 cm^2.
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