Question

A cube-shaped planter holds 27/729 cubic feet of potting soil. What is the side length of the planter?

Answer 1

Amount of potting soil present in cube shaped planter = $\frac{27}{729}$ cubic feet

Volume of a cube with side side length 'a' is given by the formula = $a^3$

Since, Volume of planter =$\frac{27}{729}$

Let the side of planter be 'x'.

So, Volume of cube planter = $x^3$

So, $x^3 = \frac{27}{729}$

$x = (\frac{27}{729})^\frac{1}{3}$

$x ={ {(\frac{3}{9})}^3}^ {\times \frac{1}{3}}$

So, $x = \frac{3}{9}$

$x = \frac{1}{3}$ feet

Therefore, the side length of the planter is $\frac{1}{3}$ feet.