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The volume of gas a balloon can hold varies directly as the cube of its radius. Imagine a balloon with a radius of 3 inches can hold 108 cubic inches of gas. How many cubic inches of gas must be released to reduce the radius down to 2 inches?

Respuesta :

Answer:76

Step-by-step explanation:

mhanifa

Answer:

  • 76 in³

Step-by-step explanation:

Volume of gas varies directly as the cube of its radius.

  • V = kr³

Find k:

  • 108 = k(3³)
  • k = 108/27
  • k = 4

Volume of the smaller balloon:

  • V = 4r³
  • V = 4(2³) = 32 in³

The difference in volumes is the volume of released gas:

  • 108 - 32 = 76 in³