Two similar solids have a surface area 48cmsq and 108 cm sq respectively.find the volume of the smaller solid if the bigger one has a volume of 162cm cubic
Question
Two similar solids have a surface area 48cmsq and 108 cm sq respectively.find the volume of the smaller solid if the bigger one has a volume of 162cm cubic
Solution
The ratio of the surface areas of two similar solids is the square of the ratio of their corresponding lengths. Similarly, the ratio of their volumes is the cube of the ratio of their corresponding lengths.
Given that the surface areas of the two solids are 48 cm² and 108 cm², the ratio of their corresponding lengths is the square root of the ratio of their surface areas.
So, √(48/108) = √(4/9) = 2/3
The ratio of their volumes is the cube of the ratio of their corresponding lengths.
So, the volume of the smaller solid is (2/3)³ times the volume of the larger solid.
Given that the volume of the larger solid is 162 cm³, the volume of the smaller solid is (2/3)³ * 162 cm³ = 8/27 * 162 cm³ = 48 cm³.
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