MathematicsA carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?

A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?


  1. A
  2. B
  3. C
  4. D
     

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    Solution:

    Let the dimensions of the first rectangular box be:
    First Box:
    Height = x
    Width = y
    Length = z
    Volume of this rectangular box is given by substituting these values in the formula:
    Volume of cuboid = Length X Breadth X Height
    Volume = xyz = 10 cubic feet
    Second box:
    Height = 2x(twice as long as the first box)
    Width = 2y (twice as wide as the first box)
    Length = 2z(twice as high as the first box)
    Volume = We know, xyz = 10 cubic feet
    Therefore, the capacity, in cubic feet, of the second sandbox is 80 cubic feet.
    So, option 3 is correct.
     
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