Question

The volume of a box is 0.001 cubic units. If the box is a cube, what is the length of one of its edges?

Answer 1

Answer: 0.1 units

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Work Shown:

0.001 = 1/1000

Apply the cube root to both parts of 1/1000 to get

`\sqrt[3]{1} = 1\\\\\sqrt[3]{1000} = 10`

So this means that,
`\left((1)/(10)\right)^3 = (1)/(10)*(1)/(10)*(1)/(10) = (1)/(1000) = 0.001`

Having a side length of 1/10 = 0.1 unit leads to a volume of 0.001 cubic units.

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A shortcut alternative is to use your calculator to get

`(0.001)^(1/3) = 0.1`

The exponent of 1/3 is the same as a cube root.