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two cubes have surface areas of 81 in.² and 144 in.² what is the ratio of the volume of the small cube to the volume of the larger cube

Sagot :

Answer is the ratio 27:64

Explanation

The surface areas are in ratio 81:144

Apply the square root to both parts to get the ratio 9:12. This ratio reduces to 3:4 when dividing both parts by the GCF 3.

The side lengths in ratio 3:4 means any of the following possibilities

  • small cube side length = 3, large cube side length = 4
  • small cube side length = 6, large cube side length = 8
  • small cube side length = 9, large cube side length = 12
  • small cube side length = 12, large cube side length = 16
  • small cube side length = 15, large cube side length = 20
  • And so on

Anyways let's return back to the ratio 3:4

To get the volume ratio, we cube both parts to go from 3:4 to 27:64

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