Question

Volume of a cubical container is 729 cubic ft. Find the length of each side of the container.

• A. 27 ft
• B. 81 ft
• C. $\sqrt[3]{39}$ ft
• D. 9 ft

Answer 1

The correct option is D 9 ft

Volume of the cubical container is $729$ cubic ft.
Let’s consider the length of each sides of the cube as $x.$
Formula to find the volume of the cube $=x^3$
That means, $x^3=729$
$\Rightarrow \sqrt[3]{3x^3}=\sqrt[3]{3729}$
$\Rightarrow x=\sqrt[3]{33\times 243}$
$\Rightarrow x=\sqrt[3]{33\times 3\times 81}$
$\Rightarrow x=\sqrt[3]{33\times 3\times 3\times 27}$
$\Rightarrow x=\sqrt[3]{33\times 3\times 3\times 3\times 3\times 3}$
$\Rightarrow x=\sqrt[3]{39\times 9\times 9}$
$\Rightarrow x=9$
Hence, the length of each side of the container $=9$ ft.

So, option D is the correct answer.