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?

Question

asked May 28, 2021 105k views

1 Answer

Gerwitz · Answer 1 · 2021-06-01T17:04:52+0000

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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.