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# The volume of the cubical tank is $125000{m^3}$. Find the length of its sides.

Last updated date: 20th Jun 2024
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Hint: Volume is measured in "cubic" units. The volume of a figure is the number of cubes required to fill it completely, like blocks in a box. Volume of a cube = side times side times side. Since each side of a square is the same, it can simply be the length of one side cube.

Volume of the tank is given to us and we know that the volume of the cubical tank will be cube of a length which in this case is unknown.
Therefore, let us consider a variable whose cube is $125000{m^3}$
Therefore,
${a^3} = 125000{m^3}$
To find the value of the length we have to solve the above equation,
Therefore,
$a = {125000^{\frac{1}{3}}}$
We can write the value of $125000$ as multiples of cubes.
Therefore,
$a = {\left( {125 \times 1000} \right)^{\frac{1}{3}}}$
$a = {\left( {{5^3} \times {{10}^3}} \right)^{\frac{1}{3}}}$
If we open the brackets, using the formula ${\left( {{a^m} \times {b^m}} \right)^{\frac{1}{m}}} = \left( {a \times b} \right)$
Therefore, on using the above formula, it becomes,
$a = 5 \times 10$
$a = 50$

Note: Make sure that you write the units.
Therefore, the lengths of the sides of the cubical tank are 50m each.