anonymous
  • anonymous
A rectangular prism (box) has dimensions of 3' by 2' by 2.5'. A new rectangular prism is formed by doubling each side of the original box creating dimensions of 6' by 4' by 5'. What is the ratio of the volume of the larger box to the smaller, similar box?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
4:1, the area of the first box 3(2)= 6, the larger one 6(4)=24 big:small 24:6 = 4:1
anonymous
  • anonymous
suppose thevolume of the smaller box is v1, and the larger is v2 the ratio of the larger to the smaller is v2/v1 v2/v1 = 3x2x2.5 / 6x4x3 = 1/8 or simply, because the new one is formed by doubling the width, height, and lenght, the new volume will be 2x2x2 (v) = 8 v therefore v2/v1=1/8
anonymous
  • anonymous
soryy it should be 8/1,not 1/8 bigger / smaller = v2/v1 =6x4x3/3x2x2.5 = 1/8

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anonymous
  • anonymous
another typo, the v2 is 6x4x5 v2/v1 = 6x4x5/3x2x2.5 = 8/1

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