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The volumes of two similar solids are 512 cm3 and 2,197 cm3. If the smaller solid has a surface area of 960 cm2, find the surface area of the larger solid.
Part I: Find the similarity ratio by taking the cube root of each volume. Show your work. (2 points)


Part II: Use your answer from Part I to find the ratio of the surface areas. Show your work. (2 points)


Part III: Set up a proportion and solve to find the surface area of the larger solid. (3 points)

Respuesta :

The similarity ratio by taking the cube root of each volume is 8/13,  ratio of the surface areas is 64/169, and surface area of the larger solid is 2535 square cm.

What is volume?

It is defined as a three-dimensional space enclosed by an object or thing.

Part 1:

Volume of larger solid = (512) cubic cm

Volume of small solid = 2197 cubic cm

Ratio of the volumes = 512/2197

Taking cube root:

Similarity ratio = 8/13

Part 2:

Similarity ratio by taking the cube root of each volume = 8/13

Taking the square of the above ratio:

= 64/169

Part 3:

64/169  = 960/SA(larger)

SA(larger) = 2535 square cm

Thus, the similarity ratio by taking the cube root of each volume is 8/13,  ratio of the surface areas is 64/169, and surface area of the larger solid is 2535 square cm.

Learn more about the volume here:

https://brainly.com/question/16788902

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