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Riya is building a staircase of cubes. She uses 1 cube on the top step, then groups of consecutive odd numbers of cubes for each later level so that each level forms a perfect cube. The first level uses 1 cube , the second uses 3 + 5 = 8 cubes , the third uses 7 + 9 + 11 = 27 cubes . How many cubes does the fourth level use?

Class 8Patterns in CubesCubes and Roots
  • A128
  • B64
  • C70
  • D58

Step-by-Step Solution

The fourth level is cubes, formed by the next 4 odd numbers 13+15+17+19 = 64.
Answer: B) 64

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