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?

# 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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