SOLUTION: The surface areas of two similar solids are 311 ft^2 and 1,037 ft^2. The volume of the larger solid is 1755 ft^3. What is the volume of the smaller solid? Also, the volume of tw
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Question 205535: The surface areas of two similar solids are 311 ft^2 and 1,037 ft^2. The volume of the larger solid is 1755 ft^3. What is the volume of the smaller solid? Also, the volume of two similar solids are 729m^3 and 125 m^3. The surface area of the larger solid is 324m^3. What is the surface area of the smaller solid?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The surface areas of two similar solids are 311 ft^2 and 1,037 ft^2. The volume of the larger solid is 1755 ft^3. What is the volume of the smaller solid?
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The ratio of area is the square of the ratio of any linear dimension.
The ratio of volume is the cube of the ratio of any linear dimension.
Linear ratio = sqrt(311/1037)
Volume ratio = (sqrt(311/1037))^3
Smaller volume = 1755*(sqrt(311/1037))^3
SV = 288.24 ft^3
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Also, the volume of two similar solids are 729m^3 and 125 m^3. The surface area of the larger solid is 324m^3. What is the surface area of the smaller solid?
Volume ratio = 125/729
Linear ratio = cube root of volume ratio = 5/9
Smaller area = 324*(5/9)^2 = 324*25/81 = 100 m^2 (you have m^3 for the area)
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