Question

$8000\sqrt[5]{58}{\text{cm}}^3$ of milk is to be fully filled in a container having equal dimensions. Calculate the height of the container.

• A. $20\sqrt[5]{52}{\text{cm}}^3$
• B. $20\sqrt[5]{52}\text{cm}$
• C. $2\sqrt[5]{520}\text{cm}$

Answer 1

The correct option is B $20\sqrt[5]{52}\text{cm}$

Volume of milk $=8000\sqrt[5]{58}{\text{cm}}^3$
Dimensions of the container are equal, therefore it is a cube.
Let's say one of the dimension is ${}^{\prime }{a}^{\prime }.$

We know, volume of cube $=a^3$
$\Rightarrow a^3=8000\sqrt[5]{58}{\text{cm}}^3$
(taking cube root in both side of the equation)
$\Rightarrow (a^3{)}^{\frac{1}{3}}=(8000\sqrt[5]{58}{\text{cm}}^3{)}^{\frac{1}{3}}$
$\Rightarrow a=(20\times 20\times 20{)}^{\frac{1}{3}}\times (\sqrt[5]{58}{)}^{\frac{1}{3}}\text{cm}$
$\Rightarrow a=20\times (8^{\frac{1}{5}}{)}^{\frac{1}{3}}\text{cm}$
$\Rightarrow a=20\times 8^{\frac{1}{3\times 5}}\text{cm}$
​​​​​​$\Rightarrow a=20\times 2^{\frac{1}{5}}\text{cm}$
​​​​​​$\Rightarrow a=20\sqrt[5]{52}\text{cm}$

$\therefore$ Height of the container is $20\sqrt[5]{52}\text{cm}.$